Book Description
Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.
Book Description
The classic reference on the theory and application of random data analysis-now expanded and revised. This eagerly awaited new edition of the bestselling random data analysis book continues to provide first-rate, practical tools for scientists and engineers who investigate dynamic data as well as those who use statistical methods to solve engineering problems. It is fully updated, covering new procedures developed since 1986 and extending the discussion to a remarkably broad range of applied fields, from aerospace and automotive industries to biomedical research. Comprehensive and self-contained, this new edition also greatly expands coverage of the theory, including derivations of key relationships in probability and random process theory not usually found in books of this kind. Special features of Random Data: Analysis and Measurement Procedures, Third Edition include:
* Basic probability functions for level crossings and peak values of random data
* Complete derivations of both old and new practical formulas for statistical error analysis of computed estimates
* The latest methods for data acquisition and processing as well as nonstationary data analysis
* Additional techniques on digital data analysis procedures
* New material on the analysis of multiple-input/multiple-output linear systems
* Numerous new examples and problem sets
* Hundreds of updated illustrations and references
*An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Customer Reviews:
Random data and Coherent content.......2000-03-28
My major is meteorology and deal with time series data, which have huge amount of data number. This book is very helpful to me. I have to determine the statistical significance of my data and check up the assumptions both in time and frequency domain, before deciding the statistical tests. I read a few this kinds of books but they were only concentrated on the explanation of simple statistics theory and then came to stop after showing only a few simple examples. So it is difficult to apply to my raw data because the assumptions that were applied to the theory were invalid in real situation. For example, ¡°Introduction to probability and statistics for engineers and scientist, by Sheldon M. Ross¡± is too theoretical to me and the application of theories is biased to the persons who are interested in small data set. Additionally, many books assumed the normal distribution and did not refer how we could test these assumptions. In analyzing the time series, not only is important the data analysis in time domain, but also the analysis in frequency domain. ¡°Applied Statistical time series analysis by Shumway¡± dealt with it. However, ¡°Random data by Bendat and Piersol¡± more will be helpful to the people who deal with time series, want to design statistical filters and to do the statistical tests and need more profound and systematic theories and understanding.
Book Description
The first part of this book presents the essential topics for an introduction to deterministic optimal control theory. The second part introduces stochastic optimal control for Markov diffusion processes. It also inlcudes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.
Customer Reviews:
Be advised . . . .......2006-03-17
Not recommended as an introduction -- lacks examples.
Average customer rating:
- Good book for learning prob and stochastics for EEs
- Wow...
- Some good some bad
- Great random processes book for engineers
- Well written but lacks editing, a bit sloppy
|
Probability and Random Processes with Applications to Signal Processing (3rd Edition)
John W. Woods , and
Henry Stark
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover
 General
| Electrical & Electronics
| Engineering
| Professional & Technical
| Subjects
| Books
General
| Industrial, Manufacturing & Operational Systems
| Engineering
| Professional & Technical
| Subjects
| Books
General
| Telecommunications
| Engineering
| Professional & Technical
| Subjects
| Books
General
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Statistics
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Stochastic Modeling
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Science
| Subjects
| Books
Probability & Statistics
| Applied
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Electrical & Electronics
| Engineering
| New & Used Textbooks
| Stores
| Books
Statistics
| Mathematics
| Sciences
| New & Used Textbooks
| Stores
| Books
General
| Mathematics
| Sciences
| New & Used Textbooks
| Stores
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Look Inside Science Books
| Trip
| Specialty Stores
| Books
Similar Items:
-
Schaum's Outline of Probability, Random Variables, and Random Processes
-
An Introduction to Signal Detection and Estimation (Springer Texts in Electrical Engineering)
-
Digital Communications
-
Discrete-Time Signal Processing (2nd Edition)
-
Introduction to Communications Engineering, 2nd Edition
ASIN: 0130200719 |
Book Description
Provides users with an accessible, yet mathematically solid, treatment of probability and random processes. Many computer examples integrated throughout, including random process examples in MATLAB.
Includes expanded discussions of fundamental principles, especially basic probability. Includes new problems which deal with applications of basic theory—in such areas as medical imaging, percolation theory in fractals, and generation of random numbers. Several new topics include Failure rates, the Chernoff bound, interval estimation and the Student t-distribution, and power spectral density estimation. Functions of Random Variables is included as a separate chapter. Mean square convergence and introduction of Martingales is covered in the latter half of the book.
Provides electrical and computer engineers with a solid treatment of probability and random processes.
Customer Reviews:
Good book for learning prob and stochastics for EEs.......2007-05-10
Used this for a course.
It is pretty good to learn the basics from, although it gets pretty deep pretty fast by the fifth chapter or so, at which point you may need to use other references to help you stay afloat. Contains a lot of good sideitems that other books don't capture, and some decent examples. Lots of emphasis on DSP, a plus if that is what you are using this material for. Yates and Goodman is good as a companion if you need help understanding the basics. Papoulis is a good companion text for the advanced stuff.
Wow..........2007-04-05
I am amazed that this book is used as a primary text at so many universities. While initially I was unsure if this was a poor text, or if I was simply not adequately prepared to take a probability course, I qucikly realized upon viewing other references that this book was useless and that there are so many other books on this subject which address probability in an intuitive manner. I sometimes read this book and wonder who the authors were writing this book for. The examples are completely overbearing in some cases. Take Example 5.5-3, which was a 4 page discourse on Black Lung, which was probably pulled out of a journal paper. While this could be an interesting topic in probability, it is frustrating, confusing and discouraging to someone trying to learn the subject. I will not even go into the books typographical errors, as they have been mentioned in several other reviews. My advice would be to check out other references if you are taking a class using this text. This book is useful only to people who have mastered the subject.
Some good some bad.......2007-01-20
I found this book to be terrible when I was looking for something specific, but good if read from the start to finish of each chapter. My style of studying doesn't mesh well with the book's lack of a useful index and procedural organization within the text. The index is useless because common, major terms refer to pages that almost exclusively off-handedly mention the term with no further explanation. This organization makes it nearly useless as a reference book.
Great random processes book for engineers.......2005-11-13
This book is ideal as a textbook in a class on random processes, particularly for engineers and those interested in signal processing and telecommunications. I have found the book very easy to follow, quite accessible and complete, and the example problems are very indicative of the approach you need to solve the exercises at the end of each chapter. I would not recommend this book for self-study, however, as I think that self-study of a subject as difficult as random processes would be tough going for anybody. The criticisms that I would make are:
1. The book is poorly edited. There are a moderate number of typos. Some are in places where it is obvious what the author meant, but a few are in critical equations that could mislead the reader.
2. There are no solutions to any of the exercises included in the book. It would really help if there were solutions to either odd or even problems included so that you would know you are on the right path.
Since Amazon does not currently show the table of contents for this book, I do so for the purpose of completeness:
Chapter one is an introduction to probability. This material is covered quickly, so the reader should just use this as a review.
Chapter two introduces random variables. Included topics are the definition of a random variable, the probability density and distribution functions. This material is presented with exceptional clarity.
Functions of Random Variables are introduced in chapter three. This is one of the hardest chapters in the book, although I have not been able to find another book that explains the same material as well. This is mainly concerned with finding the probability density functions of f(x) and f(x,y) given the pdf of the input functions. Convolution and multiple integrals abound in this chapter.
Chapter 4 is Expectation and Introduction to Estimation. This sounds straightforward, but the material on conditional expectation can get complex, although the book covers it well.
Chapter 5 is Random Vectors and Parameter Estimation. This chapter takes concepts from numerical linear algebra and applies it to random processes.
Chapter six is random sequences and introduces linear systems concepts and markov processes.
Chapters seven and eight talk about advanced concepts in random processes.
Chapter nine discusses applications of the previous eight chapters to statistical signal processing.
To get the most out of this book you should already be familiar with probability theory, multiple variable calculus, and linear algebra. If you are not, there is no way you are going to understand this material. A good companion to this book is Schaum's outline of Probability, Random Variables, and Random Processes. It covers most of the same material as this book, except that it does so with more of a mathematician's viewpoint. The Schaum's outline's solved problems also help offset the fact that there are no solutions to exercises in this book. Just remember that there is no textbook on a subject as complex as random processes that is going to negate the need for an instructor of exceptional ability.
Well written but lacks editing, a bit sloppy.......2005-03-13
This book is well written, and is especially interesting for electrical engineers because it uses examples from their field almost from the start. However, it is rife with typos, which can be frustrating in a math book, where you often assume its true, then try to figure out why. Also, it exhibits the sloppy math style common to engineers, especially when it comes to the distinction between constants and variables. This can lead to alot confusion at first.
Book Description
The Wharton School course on which the book is based is designed for energetic students who have had some experience with probability and statistics, but who have not had advanced courses in stochastic processes. Even though the course assumes only a modest background, it moves quickly and - in the end - students can expect to have the tools that are deep enough and rich enough to be relied upon throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more demanding development of continuous time stochastic process, especially Brownian motion. The construction of Brownian motion is given in detail, and enough material on the subtle properties of Brownian paths is developed so that the student should sense of when intuition can be trusted and when it cannot. The course then takes up the It¿ integral and aims to provide a development that is honest and complete without being pedantic. With the It¿ integral in hand, the course focuses more on models. Stochastic processes of importance in Finance and Economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. The financial notion of replication is developed, and the Black-Scholes PDE is derived by three different methods. The course then introduces enough of the theory of the diffusion equation to be able to solve the Black-Scholes PDE and prove the uniqueness of the solution.
Customer Reviews:
A Beautiful MATH Book.......2006-06-21
Before I write this review, it's only fair to disclose that before even hearing of it I already had a very solid background in (graduate-level) analysis, which as another reader astutely pointed out is often considered "calculus" in the math community (I think the classic Calculus by Shlomo Steinberg, which can be found free online, has been used at Harvard for decades, while Tom Apostol's "Calculus," a misnomer to say the least, is the standard text at Stanford and Cal Tech - both are really books on advanced calculus and elementary real analysis). Part of the reason I am writing this is to clarify the distinction - many people aspiring towards quantitative roles on Wall Street don't know exactly what the mathematical prerequisites are for a particular subject or presentation, and hopefully I can help clarify this for other readers who, like myself, sought books like this one to learn the basics of mathematical finance.
On that note, Steele's book is a MATH book. By contrast, the wonderful book by Baxter & Rennie emphasizes core ideas with emphasis on the relationship between the three primary tools of the discipline (Martingale Representation, Ito-Doeblin Calculus, and the Feynman-Kac formula) while Shreve's classic emphasizes actual development of key models and techniques. Even Oksendal, which is aimed at a slightly more sophisticated mathematical audience, emphasizes applications at the expense of elegance.
In contrast, Steele's book is a math book aimed at Wharton (read: finance and economics doctoral students, likely in their second year) students with varied interests. Students taking this course probably have already taken a rigorous course in asset pricing theory from the academic viewpoint and need to fill in the blanks with the continuous-time techniques to extend these techniques and to understand stochastic calculus at the level necessary for research in economics/finance.
With that in mind, the book is versatile enough to be appreciated by different audiences. Steele certainly takes care give a clear, well-motivated presentation which explains to the reader WHY he is giving a concept, proof, or problem, and breaks the book up into small, digestible chapters. The problems are neither overly difficult nor disconnected from the text, although doing them is not an essential part of understanding the overall view. Furthermore, Steele clearly takes delight in the beauty of stochastic calculus, as demonstrated by Chapter 5 - Richness of Paths, which discusses the "interesting" properties of Brownian motion. For anyone who sat through a difficult analysis class thinking the whole purpose of the course was to annoy and taunt the student with irrelevant counterexamples (remember constructing a continuous yet non-differentiable function using limits?), this chapter will be especially fun.
In the first part of the book, Steele covers the basics of the random walk and martingales, introducing important theorems such as the upcrossing (downcrossing) lemma, submartingales and the Doob Decomposition theorem, the basic martingale inequalities, stopping times, and conditional probability (for those who are familiar with Williams' Probability with Martingales, the treatment is similiar). He then covers Brownian motion from both the standard perspective (a Brownian motion is a process such that...) and more intuitively as a limit of random walks (i.e. the "wavelet" construction/proof), using this subject as an opportunity to extend the martingale concepts to continuous-time.
In what could roughly be called the "second" part of the book, Steele develops the Ito integral as a martingale and as a process. Steele provides a lot of detail to the subject, perhaps in mind with the view that readers using stochastic calculus with more general underlying processes will have to understand the difference between a martingale and "just" a local martingale. He then quickly but sufficiently covers the standard topics of Ito calculus - Ito's lemma, quadratic variation, and the basic SDE, although in the Picard-type existence/uniqueness proof of SDEs he shows why the careful description of the Ito integral is not simply technical.
The next part of the book covers the "standard" topics in financial mathematics that would appeal to quant finance students . The chapter on arbitrage covers the basic Black-Scholes-Merton equation and its generalization to arbitrage pricing, although Steele (appropriately) addresses Black and Scholes CAPM derivation of their options pricing formula, which gives the finance/economics reader a historical perspective. The chapter on diffusions is excellent and gives all of the necessary elements for handling "nice" parabolic second-order equations. He even sneaks in Green's functions, series expansions, and the Maximum Principle without making uninterested readers have to learn them to follow the presentation.
In the last few chapters, he covers Martingale Representation, Girsanov's Theorem and their applications to more advanced topics in pricing, such as forward measures. The problems in this part of the book are nice because they help the reader understand the intuition behind a particular mathematical principle but not necessarily its application to a well-recognized model. The final chapter on the Feynman-Kac formula gives a very intuitive proof of its topic which helps the reader understand what is meant by "killing" a process and hopefully how that translates into finance; other books often just do a coefficient-matching proof, which really doesn't capture what's really going on.
I emphasize again that while the book is designed to serve a different purpose than texts such as Shreve or Baxter & Rennie, it can help readers of different backgrounds understand the basic elements needed for more advanced stochastic analysis and gain an appreciation for both the beauty of the subject and the underlying intuition liking the math to the finance. The prerequisite, though, is at least a (rigorous undergrad) course in real analysis, probably some familiarity with measure theory, probability, and L(p) spaces (or at least L(1,2,inf) spaces), and at least basic familiarity with the elements of stochastic calculus (Ito's lemma and computations with "box calculus", for example). For readers seeking a more comprehensive treatment of quantitative finance, this book is reasonably good mathematical preparation to understand Musiela/Rutkowski, and for doctoral students, understanding most of the topics in this book with a brief introduction to dynamic programming in the continuous-time setting is sufficient background to read Merton's book (consumption-investment problems) as well as understand the basics of derivative pricing.
Good book.......2006-04-23
This is a good start.
One thing about mathematical prerequisitives and a pet peeve.
In general, when mathematicians state that a minimal prerequistive is calculus, they are not refering to the calculus that a science major such as a physicist would study... as David Hilbert once said, Physics is too hard for physicists...this is engineering calculus... this is geared toward usage and application( they are consumers of math). What a mathematician is refering to when they mention calculus is actually analysis...the study of limits, etc. You should be comfortable with topological concepts such as compact sets, open and closed sets, limits, epsilon-delta notation, etc, etc.
So you should keep this in mind. So if you have had a course in classical analysis and a course in probability which makes use of this background, you should have no problem with this book.
But if you are a typical engineer, physicist ( whether PHd or not ) and have never been exposed to the concept of a compact set, or group theory, etc, etc, then you need to do some homework. You will of course have the brain power...you just need the lingo and the concepts...you have probably learned the material but just don't know the math speak for it.
The type of "calculus" book I am thinking of are books such as 'Elementary Classical Analysis' by Jerrold Marsden ( my freshman "calculus" book, or 'Real Analysis' by Royden ( my sophomore "calculus" book ). By all means don't give up...but if you are planning a serious career in quantitative finance, you should master the concepts in these books. They will go a long way to help you master modern economics & finance. This book will too.
I Hate It When Books Lie About Mathematical Requriements.......2003-05-03
The book says that its only prerequisites are calculus and probability. This is not true. To be able to understand everything that's going on, you'll need to have a very good grasp of subjects like measure-theoretic probability, Hilbert spaces, and functional analysis. I quit reading the book in the early chapters, when Steele starts talking about things like "spans" and "denseness" for function spaces. I don't know where you went to school, but at my school, I didn't learn these subjects in my intro calculus and probability classes. To summarize, don't buy this book if you don't know measure theory.
If you want to learn quant finance at an elementary level, Baxter and Rennie is much, much better. Moreover, if you're comfortable with measure theory,and you want to learn the math that's necessary for option pricing, you'd be better off buying Oksendal's excellent book, which is at least as rigorous as Steele's book but much more clear.
Riskfree profit !!.......2003-03-09
The book is at the interface of three areas, math, statistics, and finance. While connections between the first two have a long history, it was the connection to finance that caught my attention. Coming from math myself, I needed first to take a closer look at the book to orient myself. The mathematical subjects, smooth sailing, include stochastic differential equations (SDE) as they relate to PDEs; and the ideas from probability and statistics include Brownian motion, martingales, stochastic processes, and the Feynman-Kac connection. Browsing the chapters I found them to be a lovely presentation of ideas with which I am familiar. For me, it was chapter 10 that turned out to have stuff that I wasn't familiar with. That is the finance part, and it is based on a model for Option Pricing developed in 1973 by Fischer Black and Myron Scholes. An arbitrage opportunity [simplified] amounts to the simultaneous purchase and sale of related securities which is guaranteed to produce a *riskless* profit. It was after reading more in this chapter I understood why the book is used in a course at the Wharton School at the University of Pennsylvania. I am impressed with the level of math in this course. Part of the motivation in the applications to finance is that arbitrage enforces the price of most derivative securities. And I learned from ch 10 that the SDE of the Black-Scholes model governs the processes which represent the two variables S, the price of a stock, and B the price of a bond, both S and B representing stochastic variables depending of time t, i.e., both stochastic processes. In the model, S is a geometric Brownian motion, and B is a deterministic process with exponential growth. The two are determined as solutions to the SDE of Black-Scholes.
Review from a grad student not at Wharton.......2003-01-29
Reading Steele's book without attending has classes at Wharton leaves the reader looking for explanations to equations. Ideas are not clearly explained and problems are not worked out in detail with a descriptive process of how to solve the problem. The brief explanations in this book intended for a reader with knowledge of calculus and probability but not having a background in Stochastic calculus do not provide a sufficient basis for the reader to learn the material.
Book Description
In recent years the growing importance of derivative products financial markets has increased the demand for mathematical skills in financial institutions. The purpose of this book is to introduce the mathematical methods of financial modelling to provide a clear explanation of the most useful models. Introduction to Stochastic Calculus begins with an elementary presentation of discrete models, including the Cox-Ross-Rubenstein model. This book will be valued by derivatives trading, marketing, and research divisions of investment banks and other institutions, and also by graduate students and research academics in applied probability and finance theory.
Customer Reviews:
Very good.......2007-07-03
I am quite familiar with this book since I enjoyed it when it was used (along with many other good books as it should) in Purdue Computational Finance program. I got to do a number of exercises from it. Some Matlab code is available on my website (click on my name above).
A very efficient book for the right audience.......2007-01-21
Introduction to Stochastic Calculus Applied to Finance, translated from French, is a widely used classic graduate textbook on mathematical finance and is a standard required text in France for DEA and PhD programs in the field.
Most folks familiar with Steve Shreve's Stochastic Calculus Models for Finance will be surprised at its brevity, for this work is aimed at different audiences.
Whereas Shreve's work is aimed at mathematicians and physicists who are coming to finance, and building on the commonalities of understandings of time series and data sets and signals, Lamberton & Lapeyre's work is aimed at an audience of mathematically trained engineers, who look at data sets as information for solving problems. Shreve's work, is, therefore, to help people come up with mathematical proofs, and L&L's is to help people solve problems.
Both probabilistic and partial differential equation approaches are covered, so both those from electrical and telecommunication engineering and mechanical engineering will be satisfied and on familiar ground. Numerical and algorithmic methods are also covered for those with systems analysis and operations management backgrounds.
This book, however, is decidedly for those who have had significant mathematical training. Whereas with Hull, Wilmott, Neftci, or Joshi you can play around with their approaches almost instantly in Excel or other programming tools (VBA, C, etc.), Lamberton and Lapeyre's work is for those who think out loud with a white board and others do the dirty work of coding. This work lacks specific examples, data sets, etc. Which makes it difficult to place. Its clarity and brevity are welcome, and it expands the knowledge beyond Hull of those who are not trained in math and came up the practical coding grunt side of quantfin. But it also is not a complete theoretical treatment for the first string math and theory set.
In short, the book is what it is: a short primer on a large area of mathematics in finance for those well-trained in a variety of engineering and applied mathematical subjects. In other words, this book is for the French, because all the best French students are always Engineers first and something else afterwards. If you also happen to be trained as an engineer and find Hull, Wilmott, Joshi & Neftci too easy, and Shreve too hard, then this is the book for you. Or if you are like me, and you've banged your head against this stuff for years just through the happenstance of your career and want to see how a mathematician writes about your gritty world, this is a great book for shedding light in areas filled with cobwebs.
Clear and concise introduction to mathematical finance........2001-07-25
This book, translated from French, is by now a classic graduate textbook on mathematical finance, and provides a clear and concise introduction to the basic and important aspects of the theory. Although one of the first textbooks on the subject, it still remains in my opinion one of the best.
The book has been written for engineering students not mathematicians and avoids the theorem/proof format, going straight to essentials.
Also, while most textbooks on mathematical finance exclusively adopt either a probabilistic (like Baxter & Rennie) or a PDE approach to the theory (Wilmott et al, Wilmott), this book maintains the balance between the two aspects. Moreover, it does not neglect numerical methods and gives details on several algorithms for option pricing ( trees, Finite Difference, Monte Carlo) Finally, and perhaps this point is very important, the book maintains a reasonable volume while treating all these topics AND maintaining a high level of scientific rigor: all statements and notations are precise and oversimplification is avoided. Advanced topics such as variational inequalities for American options and HJM theory of interest rates are also included.
Some drawbacks of the book are: - a complete absence of empirical data/ real life figures - no description of various kinds of derivative products, why they are used,... But then, what can you ask for in such a small volume?
If you are an engineering/maths student and you want to discover what mathematical finance is about, I recommend you this book instead of John Hull's book.
A good INTRODUCTION to ONE part of finance.......1999-03-14
As precisely mentioned in the title, this book is only an introduction; and it is not an introduction to finance, but to stochastic calculus applied to finance.
The buyer of this book should therefore be aware of three facts:
1. After having read this book you are not (yet) an expert on stochastic calculus applied to finance. You have to continue with other books mentioned in Lamberton/Lapeyre. But this book is an excellent framework that leads you to many important results, omiting proofs that are only technical.
2. Mathematics is used in many other areas of Finance too (Time Series Analysis for example). What is treated in this book is only a very small part of Finance Mathematics, but an important one.
3. One should read another book with more economic background at the same time.
The authors begin with discrete-time models to present many important ideas in a (mathematically) simple environment before treating the contiuous models. Introduction to stochastic integration and stochastic differential equations is brief. Stochastic integration is only with respect to the standard browning motion. After having reached the Black-Scholes model and american options, the approach via partial differential equations is treated, followed by interest rate models, models with jumps and, a good idea: a chapter on simulations.
The book has very few mistakes, no important ones, only a strange layout failure on pages 6 to 7.
So I highly recommend this book as an INTRODUCTION to ONE important part of finance mathematics if read in combination with another book with more economic background. It can especially be used for upper graduate student seminars or as a basis for lecture courses.
A stochastic approach of finance for engineers!.......1998-07-28
The french initial version of this book has been one of my first technical papers that deal with stochastic calculus towards finance. It is written by and for engineers I must admit, but students in actuarial sciences (like me) won't be lost by so many formulas and equations if they agree to read with a piece of paper and a pencil on the hand. I have worked on the Vasicek's model and the simulations described have helped me a lot. Too bad that the lattice model is not explored. Anyway it is a good preparation before the opening of "Brownian Motion and Stochastic Calculus" from Karatzas & Shreve.
Book Description
This text stresses modern ideas, including simulation and interpretation of results. It focuses on the aspects of probability most relevant to applications, such as stochastic modeling, Markov chains, reliability, and queuing.
Customer Reviews:
Elementary.......2005-12-23
I used this book for a sophomore course in probability. The major problems with this book are:
(1) Lack of mathematical rigour.
(2) Almost all of the exercises are trivial.
If you want to learn real probability look elsewhere.
Better books are available.......2002-04-06
This book, although comprehensive, does not have great appeal. It does not explain all the topics completely by giving several examples. The cover is the best part.
Excellent Textbook on Probability.......2002-01-15
This is an excellent textbook on probability. i especially like the introduction for each topic as it presents the practicality of its use in real life. Also the examples makes the topic very clear and one should come away with a good understanding of each chapter. Highly recommended!
It's good........1999-03-21
Yo. I'm one of the writer's sons. If I would of read the book, I'm sure it would be great.
Book Description
- Unique in its survey of the range of topics.
- Contains a strong, interdisciplinary format that will appeal to both students and researchers.
- Features exercises and web links to software and data sets.
Download Description
- Unique in its survey of the range of topics.
- Contains a strong, interdisciplinary format that will appeal to both students and researchers.
- Features exercises and web links to software and data sets.
Customer Reviews:
Great book!!!.......2004-12-07
A must have for anyone interested in otimization! Extremely well written and objective.
Recommended to scholars and graduate students.......2003-09-23
Introduction to Stochastic Search and Optimization provides comprehensive, current information on methods for real-world problem solving, including stochastic gradient and non-gradient techniques, as well as relatively recent innovations such as simulated annealing, genetic algorithms, and MCMC. It is written to be read and understood by graduate students, industrial practitioners, and experienced researchers in the field. Web links to software and data sets, and an extensive list of references of the book allows the reader to explore deeper into certain topic areas. I also found the index to be very comprehensive and carefully done. The appendices are as a refresher and summary of much of the prerequisite material. The book is somewhat unique in providing a balanced discussion of algorithms, including both their strengths and weaknesses. The book is among very few books that have integrated essential parts of statistical fields with optimization and decision making. The book's inclusion of a chapter on optimal experimental design is an example of such integration. The approaches discussed in the book could be used for financial decision making, forecasting, and quality improvement, among many other areas.
Book Description
The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing with them. To help the reader develop an intuitive understanding and hand-on numerical skills, numerous exercises including PC-exercises are included.
Customer Reviews:
Excellent.......2002-04-10
This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve the relevant equations of interest. Since it emphasizes the numerical solution of stochastic differential equations, the authors do not give the details behind the theory, but references are given for the interested reader.
As preparation for the study of SDEs, the authors detail some preliminary background on probability, statistics, and stochastic processes in Part 1 of the book. Particularly well-written is the discussion on random number generators and efficient methods for generating random numbers, such as the Box-Muller and Polar Marsaglia methods. Both discrete and continuous Markov processes are discussed, and the authors review the connection between Weiner processes (Brownian motion for the physicist reader) and white noise. The measure-theory foundations of the subject are outlined briefly for the interested reader.
Part 2 begins naturally with an overview of stochastic calculus, with the Ito calculus chosen to show how to generalize ordinary calculus to the stochastic realm. The authors motivate the subject as one in which the functional form of stochastic processes was emphasized, with Ito attempting to find out just when local properties such as the drift and diffusion coefficients can characterize the stochastic process. The Ito formula is shown to be a generalization of the chain rule of ordinary calculus to the case where stochasticity is present. The authors are also careful to distinguish between "random" differential equations and "stochastic" differential equations. The former can be solved by integrating over differentiable sample paths, but in the latter one has to face the nondifferentiability of the sample paths, and hence solutions are more difficult to obtain. The authors give many examples of SDEs that can be solved explicitly, and prove existence and uniqueness theorems for strong solutions of the SDEs. And since ordinary differential equations are usually tackled by Taylor series expansions, it is perhaps not surprising that this technique would be generalized to SDEs, which the authors do in detail in this part. They also outline the differences between the Ito and Stratonovich interpretations of stochastic integrals and SDEs.
Part 3 is definitely of great interest to those who must develop mathematical models using SDEs. The authors carefully outline the reasons where Ito versus the Stratonovich formulations are used, this being largely dependent on the degree of autocorrelation in the processes at hand. The Stratonovich SDE is recommended for cases when the white noise is used as an idealization of a (smooth) real noise process. The authors also show how to approximate Markov chain problems with diffusion processes, which are the solutions of Ito SDEs. Several very interesting examples are given of the applications of stochastic differential equations; the particular ones of direct interest to me were the ones on population dynamics, protein kinetics, and genetics; option pricing, and blood clotting dynamics/cellular energetics.
After a review of discrete time approzimations in ordinary deterministic differential equations, in part 4 the authors show to solve SDEs using this approximation. The familiar Euler approximation is considered, with a simple example having an explicit solution compared with its Euler approximate solution. They also show how to use simulations when an explicit solution is lacking. The importance notions of strong and weak convergence of the approximate solutions are discussed in detail. Strong convergence is basically a convergence in norm (absolute value), while weak convergence is taken with respect to a collection of test functions. Both of these types of convergence reduce to the ordinary deterministic sense of convergence when the random elements are removed.
The discussion of convergence in part 4 leads to a very extensive discussion of strongly convergent approximations in part 5, and weakly convergent approximations in part 6. Stochastic Taylor expansions done with respect to the strong convergence criterion are discussed, beginning with the Euler approximation. More complicated strongly convergent stochastic approximation schemes are also considered, such as the Milstein scheme, which reduces to the Euler scheme when the diffusion coefficients only depend on time. The strong Taylor schemes of all orders are treated in detail. Since Taylor approximations make evaluations of the derivatives necessary, which is computational intensive, the authors discuss strong approximation schemes that do not require this, much like the Runge-Kutta methods in the deterministic case , but the authors are careful to point out that the Runge-Kutta analogy is problematic in the stochastic case. Several of these "derivative-free" schemes are considered by the authors. The authors also consider implicit strong approximation schemes for stiff SDEs, wherein numerical instabilities are problematic. Interesting applications are given for strong approximations for SDEs, such as the Duffing-Van der Pol oscillator, which is very important system in engineering mechanics and phyics, and has been subjected to an incredible amount of research.
More detailed consideration of weak Taylor approximations is given in part 6. The Euler scheme is examined first in the weak approximation, with the higher-order schemes following. Since weak convergence is more stringent than strong convergence, it should come as no surprise that fewer terms are required to obtain convergence, as compared with strong convergence at the same order. This intuition is indeed verified in the discussion, and the authors treat both explicit and implicit weak approximations, along with extrapolation and predictor-corrector methods. And most importantly, the authors give an introduction to the Girsanov methods for variance reduction of weak approximations to Ito diffusions, along with other techniques for doing the same. Those readers involved in constructive quantum field theory will value the treatment on using weak approximations to calculate functional integrals. The approximation of Lyapunov exponents for stochastic dynamical systems is also treated, along with the approximation of invariant measures.
Book Description
This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of
A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.
Customer Reviews:
very good book on stochastic process.......2007-08-23
This is a very good book you don't want to miss for studying stochastic processes.
A great book........2006-12-17
You know who your real friends are when they recommend you this book. This gem gives you a real appreciation for what is, unfortunately, the "old" - style of mathematics. Unlike the disasterous expositions in certain modern texts that will remain namesless - this text motivates all its topics with ample examples and doesn't beat you over the head with notation, jargon and arrogance. The topics are appropriate for a first course and for people that want to apply the material to their work or research right away.
sequel to a first course.......2001-04-18
Karlin and Taylor wrote a classic text on stochastic processes in their "A First Course in Stochastic Processes". The second edition of that text was published in 1975. This sequel came out in 1981. It is not only a second course but it is also intended as a second volume on a larger course in stochastic processes. The authors show that they are continuing from teh first course by picking up with Chapter 10 after the first book ended with Chapter 9. Many of the topics in the first book are continued in this text including Markov chains and Diffusions. Heavy emphasis is placed on point processes and their applications including Poisson and compound Poisson processes, population growth models and queueing processes.
A MUST-HAVE IF YOU WANNA GO TO WALLSTREET!.......2000-04-22
In financial derivatives, people are generally dealing with all kinds of stochastic processes. This second course focuses on diffusion processes and prepares one with adequate knowledge to go ahead and understand how options are priced. This book itself does not touch any financial theory and will be of great use to people in genetics, mathematics and physics alike (finance also, of course). The authors give a chart of logical dependence of all the chaptors so you do not need to read every single corner if you are only interested in a specific topic. Readers are assumed to know Calculus and some basic probability theory. Knowledge of Brownian motion is not required and the authors succeded in keeping the math accessible. Although a mature senior might undertake this book, math in this book is not sloppy at all. Another thing I liked this book very much is there are so many excersices at the end of each chapter and one can check if he understands the materials or not. It's quite fair to give this book five stars.
Books:
- An Introduction to Quantum Field Theory (Frontiers in Physics)
- Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn
- Applied Partial Differential Equations, Fourth Edition
- Axiomatic Design: Advances and Applications (The Oxford Series on Advanced Manufacturing)
- Brief Calculus: An Applied Approach
- Celebrations of Death: The Anthropology of Mortuary Ritual
- Classical Dynamics of Particles and Systems
- Classical Dynamics of Particles and Systems
- Classical Dynamics of Particles and Systems
- Classical Electrodynamics Third Edition
Books Index
Books Home
Recommended Books
- Andy Goldsworthy: A Collaboration with Nature
- The Whole Foods Allergy Cookbook: Two Hundred Gourmet & Homestyle Recipes for the Food Allergic
- The Devil and Miss Prym: A Novel of Temptation
- The Industrial Revolution, 1760-1830
- The Dirt: Confessions of the World's Most Notorious Rock Band
- Theories of Everything: Selected, Collected, and Health-Inspected Cartoons, 1978-2006
- The Reef Aquarium: A Comprehensive Guide to the Identification and Care of Tropical Marine Invertebr
- Gambia Business Law Handbook
- The New Professional: Everything You Need to Know for a Great First Year on the Job
- ''TAL COMO FUE''
