Book Description
This user-friendly resource will help you grasp the concepts of probability and stochastic processes, so you can apply them in professional engineering practice. The book presents concepts clearly as a sequence of building blocks that are identified either as an axiom, definition, or theorem. This approach provides a better understanding of the material, which can be used to solve practical problems.
Key Features:
- The text follows a single model that begins with an experiment consisting of a procedure and observations.
- The mathematics of discrete random variables appears separately from the mathematics of continuous random variables.
- Stochastic processes are introduced in Chapter 6, immediately after the presentation of discrete and continuous random variables. Subsequent material, including central limit theorem approximations, laws of large numbers, and statistical inference, then use examples that reinforce stochastic process concepts.
- An abundance of exercises are provided that help students learn how to put the theory to use.
Customer Reviews:
Pretty Good Book.......2007-09-26
So i bought this book for my engineering probability class. the book is very concise and not as boring as alot of other books I read. Sometimes though its like the material is too vague at times. Sometimes the material is presented rather awkwardly with things like variance coming after all the different types of families of random variables. A good older reference book that has more information should be accompanied with this in case there is some minor confusion. It is still a pretty decent book though you just need a reference every once in a while. The matlab sections at the end of each chapter are pretty neat especially if you are going into an area of engineering with porbability involved and using matlab to model.
Best book on the subject I have come across.......2007-03-23
I have taken three classes on this subject, and I am confident in my recomendation of this text. For a first year M.S. class, I had the misfortune of having the instructor use Stark and Woods, which is overly complicated, dense, and in my opinion, the authors attempt to make the subject more difficult than it really is by including advanced topics, such as parameter estimation, in introductory chapters. This book, on the other hand, goes over all the basics in a very clean and presentable manner. I picked up this book during the class using Stark and Woods, and my performance increased drastically. This is an excellent reference and text for self study. A real life saver as well. Only complaint: it would be nice to have solutions to select problems. Most people will tell you that the only way to learn the subject is through practice, but as far as learning pricipals, this book is spot on.
A better book to understand Probability and Random Processes.......2006-04-16
I have gone through many books, including the one by Papoulis, to understand the concepts behind Random processes. There was one of the 2 problems in each book: Either the explanation was very poor with very less examples Or the book was too mathematical. No book has addressed and corrected the 2 problems completely till now to my knowledge. But, this book has tried to provide very good reading for any person in electrical engineering as the name itself suggests. Highly recommended for students to have a quick grasp of the subject.
NOT THE BEST OUT THERE.......2005-09-21
I gave this book 1 star because it is not the worst, but it is far from the best. This book is not a good book for an undergradute EE student desiring to really learn the subject.
Although the author claims that this is a friendly introduction, it is far from that. The first disappointment about this book is the introduction. The author mentioned how difficult the subject is. This in itself is discouraging for any sincere student really wanting to learn the subject. Secondly the coverage of random variables is bad, especially the single random variables. He made two poor decisions, first by seperating discrete and continous random variables. This approach confuses many students, because most engineering students can understand the calculus more than the dicrete math. If he feels that seperation is necessary then continous random variables should have been presented first. Finally no answers to any of the problems. That is a silly policy, how in the can students get feedback on their progress in the subject. I sincerely hope that professor Yates is not arrogant and will at least consider my comments. Lastly the textbook written by Richard H. Williams is the best ever written on the subject. Many arrogant professors will probably look down on his textbook because he actually teaches and explains the subject better than most.
A supportive reader.......2005-01-13
Let me begin by saying this book is written at a level for senior level B.S. and first year M.S. engineering (not math) students. It is the best book I've seen for introducing probability, random variables and related concepts to this student demographic (particularly to Elec. Eng. or Comp. Eng majors). It has all the introductory concepts and lays out the foundation for later subject matter in a seemless, easy to read and friendly manner. To qualify this statement, let me say that I had taken a similar engineering-related probability course in school a few years back that covered most of the same topics found in the Yates and Goodman book. I was confused about several issues even after I completed the course. It wasn't until I found this text and began reading it that all the questions and doubts I'd had went away. This text doesn't cover more advanced probability related concepts like entropy, mutual information and a host of others. What it does do is clearly provide you with the foundation in probability so that you can later read other more "involved" books like Stark and Woods or Papoulis and Pillai without the agony.
Book Description
This concise, informal introduction to stochastic processes evolving with time was designed to meet the needs of graduate students not only in mathematics and statistics, but in the many fields in which the concepts presented are important, including computer science, economics, business, biological science, psychology, and engineering. With emphasis on fundamental mathematical ideas rather than proofs or detailed applications, the treatment introduces the following topics:·Markov chains, with focus on the relationship between the convergence to equilibrium and the size of the eigenvalues of the stochastic matrix·Infinite state space, including the ideas of transience, null recurrence and positive recurrence·The three main types of continual time Markov chains and optimal stopping of Markov chains·Martingales, including conditional expectation, the optional sampling theorem, and the martingale convergence theorem·Renewal process and reversible Markov chains·Brownian motion, both multidimensional and one-dimensionalIntroduction to Stochastic Processes is ideal for a first course in stochastic processes without measure theory, requiring only a calculus-based undergraduate probability course and a course in linear algebra.
Customer Reviews:
Wonderful Introduction to the subject.......2007-05-14
When I was a grad student in the early 90's, the only available texts for this subject were Hoel, Port and Stone's third volume and Phillip Protter's book. The problem was that Hoel, Port and Stone was too intuitive, and Prottor was too formal.
This book is just right. The examples are well thought out, and the presentation of the subject matter is effecient without being sparse. The segue from the intuitive concept to the formal definitions / proofs is almost seemless.
I would recommend this book to anyone who wishes to learn about stochastic processes. Glad I found it!
More than precise in every aspect.......2002-11-24
This is one of the best books I've ever read in Stochastic Processes. Prof. Lawler presents Markov Chains (Finite, Countable and Continuous), Optimal Stopping, Martingales and Brownian motion concisely and straight to the gist of the subject. The exercises set at the end of each chapter fall into 2 categories: for people who read the book well and actually understand what has been stated, and to people who have a thorough understanding of solid probability theory (harder exercises).
Furthermore, it is such a small book that makes me wonder how so many information could fit in there.
The only small drawback is the few typos which can be picked up easily by the diligent reader.
In total is an extremelly good book, especially for people that haven't had an extensive contact w/ the subject before (or even measure theory), without losing any point of precision whatsoever.
An Excellent Book.......1998-09-16
In a very concise and clear way, this book gives readers all need to know in stochastic processes. It is very successful in approaching all problems and theorems without any measure theory. Great for students with all kinds of math background.
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
- 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
An excellent introduction for electrical, electronics engineers and computer scientists who would like to have a good, basic understanding of the stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.
Customer Reviews:
Good book.......2007-10-05
I used this book for my Stochastic class. In my opinion, this is a good book to start.
mediocre.......2003-09-08
I found this book to be terse and unfriendly. I used this text for my introduction to markov chains class and did not get much out of it. If ur looking for a review of markov chain theory then U should consider this book. If ur looking for clear in-depth explanations and problems that are relevant to the chapters material look somewhere else.
I learned stochastic processes from this book.......2000-12-19
Hoel, Port and Stone put together a three volume series on probability, statistics and stochastic processes. In 1975 I took the first year graduate course in stochastic processes and my Professor at Stanford Yash Mittal elected this text for the course out of a number of possibilities. This book was particularly good for an introduction to Markov chains, the backbone to stochastic processes. I learned a lot from it and found it easy to use as a text. I then bought the other to books to complete the trilogy. At the time Hoel and Port were at UCLA and I believe Stone was already at Berkeley.
This is an excellent text for a graduate course that stands the test of time. If it has been revised, I am not familiar with the new edition and any possible changes that may have occurred.
Great Books in a row.......2000-08-16
This is the last volume of a series of three excellent texts by Hoel/Port/Stone on probability, statistics and stochastic processes. The way they write should be the standard for all of other authors. Concise, clear and intuitive. Lots of worked examples and exercises with answers help readers go through those topics. If you are lack of knowledge in probability and want to know stochastic processes or even financial mathematics. These three books can be your short cut.
Excellent book........2000-04-29
If you want to learn about Markov Chains in a non-measure theoretic level, this book is a must-have. But you need to have something in probablity before, as you are supposed to for Markov Chains.
It made no mistakes. Enjoyable. Exercise problems are good, although somewhat easier than Ross's Stochastic Processes. But the contents are definitely better.
If you find this too difficult, may be you need:
1. Basic probability or 2. Basic math (how to read/write proofs) 3. and Good sleep, good dinner, good shower, lots of determination/motivation, a girlfriend too maybe.
Note: put parentheses on 1 and 2. :)
Average customer rating:
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The Quantum Dice: An Introduction to Stochastic Electrodynamics (Fundamental Theories of Physics)
Luis de la Peña , and
A.M. Cetto
Manufacturer: Springer
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ASIN: 0792338189 |
Book Description
In spite of the impressive predictive power and strong mathematical structure of quantum mechanics, the theory has always suffered from important conceptual problems. Some of these have never been solved. Motivated by this state of affairs, a number of physicists have worked together for over thirty years to develop
stochastic electrodynamics, a physical theory aimed at finding a conceptually satisfactory, realistic explanation of quantum phenomena.
This is the first book to present a comprehensive review of stochastic electrodynamics, from its origins to present-day developments. After a general introduction for the non-specialist, a critical discussion is presented of the main results of the theory as well as of the major problems encountered. A chapter on stochastic optics and some interesting consequences for local realism and the Bell inequalities is included. In the final chapters the authors propose and develop a new version of the theory that brings it in closer correspondence with quantum mechanics and sheds some light on the wave aspects of matter and the linkage with quantum electrodynamics.
Audience: The volume will be of interest to scholars and postgraduate students of theoretical and mathematical physics, foundations and philosophy of physics, and teachers of theoretical physics and quantum mechanics, electromagnetic theory, and statistical physics (stochastic processes).
Book Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. The new feature of this 5th edition is an extra chapter on applications to mathematical finance.
Customer Reviews:
A very good book!.......2007-07-05
I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.
With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!
Excellent introduction on Stochastic Differential Equations.......2007-05-08
A well written book in Mathematics
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.
OK intro to stochastic analysis.......2007-03-14
This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.
First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.
Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.
I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).
Very good book - would not mind more on finance.......2007-02-08
Very good book. However the math prerequisite is at quite a high level. Especially the probability theory introduction could be a little less fast-paced. As my main interest was on the financial application I would not have minded a little more on that topic and a little less on e.g. filtering or stochatsic control in return.
good intro book.......2006-02-03
This is a good intro book. It brings you really fast to Ito's Formula and SDE. Somebody said that the Kolmogorov's backward eq in chapter 8 is wrong. This is false, it is just expressed in a different way than the usual form. However, with a change of time, you are all set.
Average customer rating:
- Dive into the deep end... or atleast pretend you are...
- Cheap Binding
- So Much Potential
- Good book overall, organization is very poor
- A very good introductory book
|
An Introduction to Stochastic Modeling, Third Edition
Samuel Karlin , and
Howard M. Taylor
Manufacturer: Academic Press
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ASIN: 0126848874 |
Book Description
Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus,
Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.
* Realistic applications from a variety of disciplines integrated throughout the text
* Plentiful, updated and more rigorous problems, including computer "challenges"
* Revised end-of-chapter exercises setsin all, 250 exercises with answers
* New chapter on Brownian motion and related processes
* Additional sections on Matingales and Poisson process
* Solutions manual available to adopting instructors
Customer Reviews:
Dive into the deep end... or atleast pretend you are..........2006-07-20
This book opens with a nose dive into Conditional probability. Unlike some other authors that devote a half their entire bloody book on review of probability, random variables, and conditional probability distributions, this book assumes a firm or atleast an introductory knowledge of the above. Ideally, a good probability book such as Hogg and Tanis would prove to be quite helpful as a supplementary reference.
Markov Chains and Processes are introduced in the third chapter and the definition is lucid, complete with examples that are easy to comprehend. One of the examples that calculated the frequency with which an autoparts store must replenish its stock was absolutely brilliant and made things a lot easier to understand. The exercises are rather thorough, so if you are purchasing this book for a class and will be assigned homework assignments from the text, be prepared to devote atleast an hour on an average to each problem.
The book is relatively easy to read, if you have a good background in random variables, and hence, i repeat, keep a book on introductory probability and statistics handy.
Cheap Binding.......2006-01-10
Letting the other reviews critique the content, I would like to mention that I was unimpressed with the quality of the binding.
Although I may be a unique occurence, the binding of my book was cheap and broke so that several pages came loose. For an $80 book I expect better durability than a paperback.
So Much Potential.......2005-10-19
I purchased this book to use as the text for a graduate level Stochastic Processes course that I am taking by independent study, and have had a large role in designing. I purchased the book, sight unseen, based on reviews that indicated there were many examples with solutions, wary that reviews also mentioned a lack of organization.
The organization was worse than I could have anticipated, and is one of two major flaws that do not render the book unusable, but make it very unpleasant to work with.
As has been mentioned, the outline numbering system makes chapters harder to follow, rather than easier, and it is difficult to distinguish the exercises with solutions from the problems with no solutions. This strange numbering system is carried out in the answer key portion, as well. When I read similar comments in reviews, I thought, how bad can it be? Creatively bad.
The most problematic organizational point, however, is the fact that concepts are covered in homework problems before they are introduced in the text. Chapter 1, for example, contains problems that could only be done after reading Chapter 2. This juxtaposition of discussion and exercise is still taking place as I am about three fourths of the way through the book.
The second issue with this text, besides the confusing organization, is the cumbersome use of notation with no key or explanation. Commonly, sections of text are only three or four pages long. They consist of, "Here is a formula. Now here is the proof," without any real explanation of what the formula is for, and perhaps, worse, no indication of what the variables stand for. The field of statistics is notorious for it's inconsistent use of symbology. Most texts address this by including a key of symbols. Not only has a key not been included in this text, but the symbology is most uncommon. It has taken me quite a bit of searching to decipher a number of symbols for which there were much more common alternatives.
In it's favor, the exercises and problems in the book are good, appropriate, and even classic examples.
With a strong enough background in probability, particularly Markov processes, or, with good instruction, this book is a decent source of exercises. But certainly there are better sources of exercises if we must look elsewhere for instruction.
Good book overall, organization is very poor.......2003-02-21
First, let me say that I found the content of this book to be, on the overall, wonderful and fairly well explained. Concepts are presented well and, unlike many other books on Stochastic Modeling, sigma algebra is avoided (this is a definant plus for making it into an undergrad or low-level grad textbook).
That having been said, this book has some of the worst organization I have ever seen in a textbook. Every chapter is divided into sections and at the end of each section there are questions which are separated into "Exercises" and "Problems"; this in-and-of itself is not as much of a problem as that everything is numbered the same way.
Therefore problem 5 in section 4 chapter 3 is numbered the same way (4.5) as exercise 5 in the same section and chapter is numbered the same way as exercise/problem 5 in the same section of any other chapter in the book. The only real difference between "Exercises" and "Problems" is that exercises tend to be answered in the back of the book.
There are also other organizational difficulties in the text itself--such as that it is never entirely clear where the examples are in the text: there are several things which are labeled as examples (and are), however, over half of the examples in some chapters seem to be simply thrown into the text without any special indicator that they are examples of what is being discussed.
While the content in this book is good, the organization is so wretched that I have to knock it down two stars.
A very good introductory book.......2000-02-10
The book shows through examples the very vast collection of stochastic models without going too deep in the technical details. I consider the book a good introduction for undergraduate students with a calculus and probability course. Most adequately for engineers than mathematicians.
Book Description
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. A whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium.
Customer Reviews:
Nice treatment of time-inhomogeneous processes.......2007-02-18
I bought this book not because I needed to learn about Markov processes (I deal with them rather often) but because I wanted a text that discussed time-inhomogeneous Markov processes, however briefly. (I have been told that Doob does this, but I can't ever seem to bring myself to put in the work necessary to really appreciate his stochastic processes book.) Stroock gives a nice treatment of this topic in the context of simulated annealing, which is probably where most people would first encounter it these days.
I have not read most of the rest of the book, but it is clearly a more rigorous treatment than either Norris or Bremaud (both of which are nice for the beginner or non-mathematician), and it requires a bit more mathematical maturity. Nevertheless my sampling indicates that it is well-written. It is probably better suited for the mathematicians and probabilists (or those who will have to deal with more advanced topics later) than for the average user of Markov processes. I would recommend it, along with Williams' wonderful Probability with Martingales, to anyone who wants a really solid yet concise grounding in mathematical probability at the undergraduate level.
The Place to Begin Understanding Stochastic Analysis.......2005-09-06
The book provides a solid introduction into the study of stochastic processes and fills a significant gap in the literature: a text that provides a sophisticated study of stochastic processes in general (and Markov processes in particular) without a lot of heavy prerequisites.
Stroock keeps the prerequisites very light. The reader need only have an understanding of some elementary topics. For undergraduate calculus, I recommend the two volume set "Introduction to Calculus and Analysis" by Courant & John. You'll also need a good understanding of basic statistic/probability theory at the level of Moore's "Mathematical Statistics", 6th edition. Make sure you have a grasp of some basic matrix algebra, at least through Eigen vectors and Eigen values of a square matrix.
Stroock begins his book with a study of 1-dimensional random walks in Chapter 1. First passage times, first return times and the reflection principle are each introduced. (You'd study precisely the same topics from the Brownian motion point of view in an advanced measure-theoretic text). Higher dimensional random walks are introduced and transience/recurrence is studied.
A study of the Markov chain begins in earnest in Chapter 2. Stroock starts this chapter by establishing the existence of discrete time Markov chains using a construction technique based on a sequence of independent, identically distributed uniform random variables. This is a simple, yet powerful technique and different versions of this are used again in the construction of the Poisson process, the time homogenous Markov process, as well as the non-homogenous Markov process. Doeblin's Stationary Distribution Theorem is established and results from Ergodic Theory for these Doeblin chains are studied.
General (non-Doeblin) Markov chains are considered in Chapter 3. Stroock studies state communication and brings this together with some tools such as Doob's Stopping Time Theorem. Ergodic results are established in this context, starting with some simple results which are then refined.
Chapter 4 is a real highlight of the book. Continuous time Markov processes with values in a countable state space are studied in depth. This chapter focuses on the time-homogeneous case and starts with the construction of Poisson processes and compound Poisson processes. The Markov property is called out at each stage. These elementary stochastic processes are then used as the building blocks for the general time-homogenous Markov process (first with bounded, then unbounded transition rates). Ergodic Theory for these processes is then studied.
Chapter 5 builds towards a principle application, which is a Markov process study of simulated annealing. To get at this application, Stroock considers reversible Markov chains, reversible Markov processes, the Dirichlet form and Poincare's Inequality for this form. Gibbs states are studied next and the discussion of equilibriums leads quite naturally to both the study of simulated annealing and an extremely nice construction of a non-homogenous Markov process suited towards this study.
Chapter 6 is a primer for Lebesgue measure theory. Although this section is certainly not comprehensive, it is quite accessible, provides an interesting 'glimpse ahead' and suggests topics for further study.
Each chapter concludes with a number of really nice exercises of varying difficulty. The author is kind enough to provide some helpful hints for the more challenging problems.
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