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Stochastic Differential Equations

An Introduction with Applications

  • Bernt Øksendal

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Bernt Øksendal
    Pages 1-6
  3. Bernt Øksendal
    Pages 7-14
  4. Bernt Øksendal
    Pages 15-31
  5. Bernt Øksendal
    Pages 32-37
  6. Bernt Øksendal
    Pages 38-50
  7. Bernt Øksendal
    Pages 51-78
  8. Bernt Øksendal
    Pages 79-119
  9. Bernt Øksendal
    Pages 120-142
  10. Bernt Øksendal
    Pages 143-170
  11. Bernt Øksendal
    Pages 171-188
  12. Back Matter
    Pages 189-208

About this book

Introduction

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.

Keywords

Differential Equations Equations Optimal Filtering Random variable Rang Stochastic Control application applications filtering problem filtering theory measure theory stochastic analysis stochastic calculus stochastic differential equation stochastic differential equations

Authors and affiliations

  • Bernt Øksendal
    • 1
  1. 1.Department of MathematicsUniversity of OsloBlindern, Oslo 3Norway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-13050-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1985
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-15292-7
  • Online ISBN 978-3-662-13050-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site