Weak Convergence and Empirical Processes: With Applications to Statistics (Springer Series in Statistics)

Book Description

This book provides an account of weak convergence theory and empirical processes and their applications to a wide variety of applications in statistics. The first part of the book presents a thorough account of stocastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of topics which demonstrate the applicability of the theory to important questions such as: limit theorems in asymptotic statistics; measures of goodness of fit; the bootstrap; and semiparametric estimation. Most of the sections conclude with "problems and complements". Some of these are exercises to help the reader's understanding of the material whereas others are intended to supplement the text.

Customer Reviews:

The best book on empirical processes........2000-03-27

It's a beautifully written book. Many useful techniques with examples of application. Great reference book. Must have in your library.

Linear Processes in Function Spaces: Theory and Applications (Lecture Notes in Statistics)

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Linear Processes in Function Spaces: Theory and Applications (Lecture Notes in Statistics)
D. Bosq
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 0387950524

Book Description

The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces.The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).

Stochastic Calculus and Financial Applications

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A Beautiful MATH Book
Good book
I Hate It When Books Lie About Mathematical Requriements
Riskfree profit !!
Review from a grad student not at Wharton

Stochastic Calculus and Financial Applications
J. Michael Steele
Manufacturer: Springer
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Binding: Hardcover

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Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Springer Finance)
Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability)
Stochastic Differential Equations: An Introduction with Applications (Universitext)
Financial Calculus : An Introduction to Derivative Pricing

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Heavy-Tail Phenomena: Probabilistic and Statistical Modeling (Springer Series in Operations Research and Financial Engineering)
A Modern Introduction to Probability and Statistics: Understanding Why and How (Springer Texts in Statistics)
Applied Stochastic Processes (Universitext)

ASIN: 0387950168

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.

Introduction to Stochastic Calculus with Applications

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Splendid text, but perhaps a bit lost in the shuffle.
A good book with yet misleading intro
Excellent introduction to stochastic processes
One of the best concise and readable books on the subject
Introduction to Stochastic Calculus with Applications

Introduction to Stochastic Calculus with Applications
Fima C. Klebaner
Manufacturer: Imperial College Press
ProductGroup: Book
Binding: Paperback

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Similar Items:

Elementary Stochastic Calculus With Finance in View (Advanced Series on Statistical Science & Applied Probability, Vol 6)
Stochastic Differential Equations: An Introduction with Applications (Universitext)
Stochastic Calculus and Financial Applications
Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance)
Options, Futures and Other Derivatives (6th Edition)

ASIN: 186094566X

Product Description

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering. Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling. This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic LotkaVolterra model in biology, non-linear filtering in engineering and five new figures.

Customer Reviews:

Splendid text, but perhaps a bit lost in the shuffle........2006-05-14

The second edition of this delightful title by Fima C. Klebaner (Monash University, Australia) is a well-written and worthwhile excursion into the realm of stochastic calculus. The text is suited for self-study for a newcomer to the area and there are numerous worked out examples interspersed throughout. Chapters 1 and 2 cover the basics of math and probability/random processes. The author next moves to discuss Brownian Motion and its calculus (the Ito calculus) in chapters 3 and 4. The coverage of the SDEs, diffusions, martingales, semi-martingales, and pure jump processes are included next. Subsequently a chapter on some results concerning the change of probability measure rounds up the theoretical part of the book. There are four final chapters (in the 2nd edition) on applications in finance (stocks, bonds, two fundamental theorems on asset pricing, discussion of various market models), biology (Feller and Wright-Fisher diffusions, branching and birth-death processes, stochastic Lotka-Volterra models) and engineering/physics (filtering and random oscillators) to help satisfy the curiosity of the application-minded readers.

The second edition contains a new chapter on bonds and interest rates, and incorporates more worked-out examples throughout. The discussion of the Stratanovich formulation of Ito's calculus has been moved from the final chapter in the first edition, to the last section of chapter 5 on SDEs. Also at the back of the book there are many answers provided to the selected exercises. For fully grasping the concepts presented, having a background in real analysis and measure theory is helpful but not completely necessary. This was my first book on the subject and it immensely helped me form a fair understanding of the concepts, techniques and terminology of the stochastic calculus. I could only guess that many of you would also benefit from taking up this title at some point in your studies. The only thing that I sensed missing was a glossary with a list of common financial terms for the benefit of those readers who come from a different background. For the science oriented readers, another suggested title is "Stochastic Calculus: Applications in Science and Engineering" by Mircea Grigoriu, which at the same time does a nice job of touching upon the all-important computational methods.

A good book with yet misleading intro.......2003-03-14

I have to agree with one of the earlier reviewers who rates the book only 3-star. As a reader from engineering background who is determined to grasp the gist of stochastic calculus, I found at the beginning this book hard to carry on. It is only after taking on some readings about theoretical probability and measure theory that I find this book enjoyable. Thus, the statement of 'only a basic knowledge of calculus and probability is required' in the preface is misleading. One has to realize what is considered 'basic knowledge' for mathematicians may not be basic for engineerings, and vice versa.

But, this is indeed an excellent book on the subject without burdening the readers with every rigorous proofs. I would have rated it 5-star if not for the misleading statement. As long as one has a basic knowledge in real analysis, indeed very basic, one will find this book highly enjoyable.

Excellent introduction to stochastic processes.......2002-12-01

This is a very nice book. Looking forward to the 2nd edition with more material particularly on interest rate models.

One of the best concise and readable books on the subject.......2002-10-01

I've seen lot's of other books, (Karatzas, Protter, etc.) but none of them were so well and concisely written. I do recommend this book to anybody who wants to get a quick but still pretty thorough intro to the matter, without spending too much time on the proofs.

Introduction to Stochastic Calculus with Applications.......2001-05-27

This is a very readable text, which is very rare for this subject. Most text on stochastic calculus and Brownian motion rely heavily on measure theory. This text only assumes a familiarity with calculus and concepts in probability theory.

Book Description

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called "randomized algorithms", this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H-infinity control.

Features:

• self-contained treatment explaining randomized algorithms from their genesis in the principles of probability theory to their use for robust analysis and controller synthesis;

• comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining independent and identically distributed samples;

• applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems.

Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.

The present book is a very timely contribution to the literature. I have no hesitation in asserting that it will remain a widely cited reference work for many years.

M. Vidyasagar

Applications of Orlicz Spaces (Pure and Applied Mathematics)

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Applications of Orlicz Spaces (Pure and Applied Mathematics)
M.M. Rao , and Z.D. Ren
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824707303

Book Description

Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.

Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming (Systems & Control: Foundations & Applications)

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Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming (Systems & Control: Foundations & Applications)

Manufacturer: Birkhäuser Boston
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ASIN: 0817640789

Spatial Objective Analysis: With Applications in Atmospheric Science

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Spatial Objective Analysis: With Applications in Atmospheric Science
H. J. Thiebaux , and M. A. Pedder
Manufacturer: Academic Pr
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Markov Chain Monte Carlo: Innovations And Applications (Lecture Notes Series, Institute for Mathematical Sciences, N) (Lecture Note)

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Markov Chain Monte Carlo: Innovations And Applications (Lecture Notes Series, Institute for Mathematical Sciences, N) (Lecture Note)

Manufacturer: World Scientific Publishing Company
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Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition (Texts in Statistical Science Series)
A Handbook of Statistical Analyses Using R

ASIN: 9812564276

Product Description

Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines.

Principles of Random Signal Analysis and Low Noise Design: The Power Spectral Density and its Applications

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Covering the gap between engineering and rigour

Principles of Random Signal Analysis and Low Noise Design: The Power Spectral Density and its Applications
Roy M. Howard
Manufacturer: Wiley-IEEE Press
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An Introduction to the Theory of Random Signals and Noise

ASIN: 0471226173

Book Description

Describes the leading techniques for analyzing noise.
Discusses methods that are applicable to periodic signals, aperiodic signals, or random processes over finite or infinite intervals.
Provides readers with a useful reference when designing or modeling communications systems.

Customer Reviews:

Covering the gap between engineering and rigour.......2007-02-28

Power Spectral Density is widespread used in electronic engineering books as the Fourier Transform of correlation functions. However this definition seems rather mysterious and not very well connected with the intuitive idea of power, specially for stochastic processes.

This books gives the definitions, proofs and motivations behind Power Spectral Density. It rigorously establishes the bridge between "engineers intuitive concepts" and mathematical laid-down definitions.

Although it introduces Lebesgue and measure theory, the first chapters of the book are not intended to mathematicians, so it only deals with those fundamental results which will be needed further in the book. In following chapters one readily get a great insight into the concepts and connections between those split worlds of engineering and mathematics. The exposition is clear even in the case of stochastic processes, where the Power Spectral Density is clearly definded as a statistical average power.

For those engineers aware of the gaps and flaws of engineering books and who can't turn a blind eye to mathematics, this is a must have book.

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