# Stochastic Differential Equations

## An Introduction with Applications

• Bernt Øksendal
Textbook

Part of the Universitext book series (UTX)

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

### 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
• Print ISBN 978-3-540-15292-7
• Online ISBN 978-3-662-13050-6
• Series Print ISSN 0172-5939
• Series Online ISSN 2191-6675
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