Oksendal Stochastic Differential Equations

An Introduction with Applications
3rd Auflage 1992
ISBN: 978-3-662-02847-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 228 Seiten, eBook

Reihe: Universitext

From the reviews to the first edition:
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 view.: Not knowing anything ... about a subject to
start with, what would I like to know first of all. My
answer would be: 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
thetheory works and to motivate the next step in the
theoretical development. Needless to say, he restricts
himself to stochastic integration with respectto 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.
From: Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986

Zielgruppe

Graduate

Autoren/Hrsg.

Oksendal, Bernt

Inhaltsverzeichnis

I. Introduction.- II. Some Mathematical Preliminaries.- III. Ito Integrals.- IV. Stochastic Integrals and the Ito Formula.- V. Stochastic Differential Equations.- VI. The Filtering Problem.- VII. Diffusions: 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 A: Normal Random Variables.- Appendix B: Conditional Expectations.- Appendix C: Uniform Integrability and Martingale Convergence.- List of Frequently Used Notation and Symbols.