Stochastic Differential Equations: An Introduction with Applications

by Bernt Oksendal

I. Introduction.- II. Some Mathematical Preliminaries.- III. Ito Integrals.- IV. Ito Processes and the Ito Formula.- V. Stochastic Differential Equations.- VI. The Filtering Problem.- VII. Basic Properties.- VIII. Other Topics in Diffusion Theory.- IX. Applications to Boundary Value Problems.- X. Application to Optimal Stopping.- XI. Application to Stochastic Control.- Appendix Normal Random Variables.- Appendix Conditional Expectations.- Appendix Uniform Integrability and Martingale Convergence.- Solutions and additional hints to some of the exercises.- List of Frequently Used Notation and Symbols.

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

288 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.

[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