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Stochastic Differential Equations

An Introduction with Applications

  • Textbook
  • © 1985

Overview

Authors:
  1. Bernt Øksendal

    1. Department of Mathematics, University of Oslo, Blindern, Oslo 3, Norway

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Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Introduction

    • Bernt Øksendal
    Pages 1-6

  3. Some Mathematical Preliminaries

    • Bernt Øksendal
    Pages 7-14

  4. ITO Integrals

    • Bernt Øksendal
    Pages 15-31

  5. Stochastic Integrals and the ITO Formula

    • Bernt Øksendal
    Pages 32-37

  6. Stochastic Differential Equations

    • Bernt Øksendal
    Pages 38-50

  7. The Filtering Problem

    • Bernt Øksendal
    Pages 51-78

  8. Diffusions

    • Bernt Øksendal
    Pages 79-119

  9. Applications to Partial Differential Equations

    • Bernt Øksendal
    Pages 120-142

  10. Application to Optimal Stopping

    • Bernt Øksendal
    Pages 143-170

  11. Application to Stochastic Control

    • Bernt Øksendal
    Pages 171-188

  12. Back Matter

    Pages 189-208
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Keywords

About this book

These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen­ tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica­ tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop­ ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete­ ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) 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? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Authors and Affiliations

  • Department of Mathematics, University of Oslo, Blindern, Oslo 3, Norway

    Bernt Øksendal

Bibliographic Information

  • Book Title: Stochastic Differential Equations

  • Book Subtitle: An Introduction with Applications

  • Authors: Bernt Øksendal

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-662-13050-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1985

  • eBook ISBN: 978-3-662-13050-6Published: 09 March 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIII, 208

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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