Stochastic Differential Equations: An Introduction with Applications (Universitext) [Paperback]

Bernt Øksendal (Author)

Book Description

Series: Universitext | Publication Date: September 22, 2010

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. The corrected 5th printing of the 6th edition is forthcoming and expected in September 2010.

Editorial Reviews

Review

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)

Product Details

• Paperback: 404 pages
• Publisher: Springer; 6th edition (September 22, 2010)
• Language: English
• ISBN-10: 3540047581
• ISBN-13: 978-3540047582
• Product Dimensions: 9.4 x 6.1 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (23 customer reviews)
• Amazon Best Sellers Rank: #48,581 in Books (See Top 100 in Books)
  • #17 in Books > Professional & Technical > Professional Science > Physics > System Theory
  • #24 in Books > Professional & Technical > Professional Science > Physics > Mathematical Physics

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Customer Reviews

Most Helpful Customer Reviews

32 of 32 people found the following review helpful:

4.0 out of 5 stars An excellent introduction to stochastic calculus, May 13, 2005

By 

J. Lim "wholewheat" (New York, NY USA) - See all my reviews
(REAL NAME)   

This review is from: Stochastic Differential Equations: An Introduction with Applications (Universitext) (Paperback)

This my recommendation for people who want to learn stochastic calculus for the first time. The virtue of this book is that it keeps matters simple,well grounded, and intuitive enough to hook the newcomers in the subject. Once you get comfortable enough and want to learn technical detail necessary for scholarly research, there are other excellent expositions such as Karatzas and Shreve(1998) and Protter(1990). Some reviews complained that this book is limited to stochastic integration with respect to Brownian motion, but that is precisely why I recommend this book. By starting with Browning motion readers can form concrete mental image of stochastic integration and get ready to stride to more general setting if necessary.
Another virtue of this book is the plenty (easy) exercise problems. Working through them is perhaps the best way to learn stochastic calculus.

32 of 33 people found the following review helpful:

5.0 out of 5 stars Simple, but rigorous book, August 17, 2000

By 

Alex Levin (New York) - See all my reviews

This review is from: Stochastic Differential Equations: An Introduction with Applications (Paperback)

This a perfectly written book on stochastic calculus, especially needed for junior (but rising!) financial quants. All themes are carried out with a profound pedagogical talent. For a practitioner, the book loses nothing to Karatsas and Shreve, but is a much shorter, simpler and joyable reading. Yet, it is a systematic text book that covers most classical results with (important!) accessible proofs. For example, the Kolmogorov equations (forward and backward) are derived, not just stated as in most other texts, Girsanov's theorem is relatively well covered (although the author has not demonstrated its computational side well enough, but this is a common disease). Ideas are illustrated by practical problems (including those from quantitative finance). What I also liked, Oksendal's SDE theory is much closer to "differential equations", than what is often presented by probabilists. A must for every practitioner who works with stochatic processes.

24 of 25 people found the following review helpful:

5.0 out of 5 stars An excellent introductory book to SDEs, November 8, 1999

By A Customer

This review is from: Stochastic Differential Equations: An Introduction with Applications (Paperback)

This is a book I recommend as a TA in a mathematical finance Masters program. It gives a mathematically rigorous presentation of Stocastic Differential Equations without getting bogged down in too much detail, as do many books from a probability/stochastic processes background. It also illustrates the beautiful connection between SDEs and the heat equation. I recommend this book to anyone trying to read Karakas and Shreve for the first time.