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. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. Apart from several minor corrections and improvements, based on useful comments from readers and experts, the most important change in the corrected 5th printing of the 6th edition is in Theorem 10.1.9, where the proof of part b has been corrected and rewritten.
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From the reviews of the fifth edition: "This is a highly readable and refreshingly rigorous introduction to stochastic calculus. … This is not a watered-down treatment. It is a serious introduction that starts with fundamental measure-theoretic concepts and ends, coincidentally, with the Black-Scholes formula as one of several examples of applications. This is the best single resource for learning the stochastic calculus … ." (riskbook.com, 2002) From the reviews of the sixth edition: "The book … has evolved from a 200-page typewritten booklet to a modern classic. Part of its charm and success is the fact that the author does not bother too much with the (for the novice) cumbersome rigorous theory … . This does not mean that the book is not rigorous, it is just the timing and dosage of mathematical rigour … that is palatable for undergraduates … . a highly readable account, suitable for self-study and for use in the classroom." (René L. Schilling, The Mathematical Gazette, March, 2005) "This is the sixth edition of the classical and excellent book on stochastic differential equations. The main difference with the next to last edition is the addition of detailed solutions of selected exercises … . This is certainly an excellent idea in view to test its ability of applications of the concepts … . certainly one of the best books on the subject, it will be very helpful to any graduate students and also very valuable for any analysts of financial market." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004) "This is now the sixth edition of the excellent book on stochastic differential equations and related topics. … the presentation is successfully balanced between being easily accessible for a broad audience and being mathematically rigorous. The book is a first choice for courses at graduate level in applied stochastic differential equations. The inclusion of detailed solutions to many of the exercises in this edition also makes it very useful for self-study." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1025, 2003)
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If we allow for some randomness in some of the coefficients of a differential equation we often obtain a more realistic mathematical model of the situation. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index
If we allow for some randomness in some of the coefficients of a differential equation we often obtain a more realistic mathematical model of the situation. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Most Helpful Customer Reviews
9 of 9 people found the following review helpful
By A Customer
Format:Paperback
I found this book very good overall. I can recommend it only for readers that are already familiar with basic probability/measure theory. Altough it doesn#t explicitly say that, it requires some decent exposure to this subject, otherwise it becomes a bit difficult to read, and can be frustrating when trying to follow his proofs.
The author has an excellent writing style; precise, clear, strict but explanatory and descriptive at the same time.
I helped me enormously to understand stochastic PDE's.
17 of 18 people found the following review helpful
By I. J. Clark
Format:Paperback
A previous reviewer described this book as having applications which are "mathematical - far from real life".
Actually, nothing could be further from the truth. Chapter 12, "Application to Mathematical Finance" demonstrates how techniques from stochastic calculus are used daily in industry to price and hedge financial derivatives. The Kalman-Bucy filter, described in Chapter 6, was an important component of the guidance systems used in the Apollo space program. These are very practical applications indeed!
This is quite simply one of the most accessible entry level texts I know for stochastic calculus. This is not to say the subject is easy - it isn't. However, a thorough study of this book will yield many rewards for the motivated reader.
The book does, hoever, presuppose a familiarity with probability and measure theory so one might consider having a good book on probability and measure theory close at hand, e.g. "Probability with Martingales" by David Williams.
By Riz
Format:Paperback|Amazon Verified Purchase
There are two dominating versions of stochastic calculus, the Ito stochastic calculus and the Stratonovich stochastic calculus. Each of the two has advantages and disadvantages, and newcomers are often confused whether the one is more appropriate than the other in a given situation. Brief guidelines exists in this book, and therefore after reading this book one can readily convert an Ito SDE to an equivalent Stratonovich SDE and back again.
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Most Recent Customer Reviews
5.0 out of 5 stars
Very good book if you need to learn the subject of SDE's
This book is very well placed on the difficulty scale. It does require some mathematical background (mainly probability and measure theory) but it does not leave the reader on... Read more
Published on 18 April 2011 by Mr. Mariusz Siomak
5.0 out of 5 stars
Decent, thorough introduction to SDEs
This book is pitched at the "first year graduate" level, meaning that it is a lot more accessible than a lot of the other books on the subject. Read more
Published on 13 Sep 2010 by Mr. W. M. Dumas
4.0 out of 5 stars
A good book for people who love the maths behind the problem
The book presents an introduction to stochastic differential equations, going in a very fast pace. However, it offers a complex view into the engineering of SDE's, but the... Read more
Published on 5 Feb 2001
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