Stochastic Differential Equations: An Introduction with Applications

by Bernt Øksendal

From the reviews to the first Most of the literature about stochastic differential equations seems to place so much emphasis on rigor and completeness that it scares the nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of Not knowing anything ...about a subject to start with, what would I like to know first of all. My answer would 1) In what situations does the subject arise ? 2) What are its essential features? 3) What are the applications and the connections to other fields?" The author, a lucid mind with a fine pedagocical instinct, has written a splendid text that achieves his aims set forward above. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications"...It can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about. Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986

Genres: Mathematics, Finance, Textbooks, Science, Physics, Academic

239 pages, Paperback

First published January 1, 1985

Reviews

[Frank Ashe · Rating 3 out of 5]

Was working in option pricing, so thought I'd better get an idea of what I was doing.

[Matthew Zhang · Rating 5 out of 5]

Better than Steele

[Dmitri · Rating 5 out of 5]

This book is the 'principal' text used by, ahem, everyone in graduate courses that relate to stochastic calculus. It is certainly not a simple text, and requires background knowledge in the areas of (at least) probability/statistics and measure theory, too. It is well structured, very readable, and is an excellent second book after reading something more rudimentary, such as Brownian Motion Calculus.

[Yan Zhu · Rating 4 out of 5]

It's a very well written book, but to appreciate this book, one still need a good understanding of graduate level probability knowledge, such as martingale, stopping time.

I took out of 1 star after i read this book up to ch10 twice. It's probably a personal reason: the author really leads me to that far in this book, but when i looked back i didn't feel much left in my head...weird?

[Jerzy]

(supposed to be one of the best intros to stochastic calculus out there)

[Alexandra Zhuk · Rating 5 out of 5]

a great introduction into stochastic differential equations! It was a textbook for the course of SDE at MIPT, prof Bulinski.

[Le Son · Rating 4 out of 5]

Arguably one of the most important books in the understanding of SDEs.

[Paul · Rating 3 out of 5]

This book is really dense