# Stochastic Differential Equations

## An Introduction with Applications

• Bernt Øksendal
Book

Part of the Universitext book series (UTX)

1. Front Matter
Pages I-XIII
2. Bernt Øksendal
Pages 1-4
3. Bernt Øksendal
Pages 5-13
4. Bernt Øksendal
Pages 14-31
5. Bernt Øksendal
Pages 32-43
6. Bernt Øksendal
Pages 44-57
7. Bernt Øksendal
Pages 58-85
8. Bernt Øksendal
Pages 86-104
9. Bernt Øksendal
Pages 105-132
10. Bernt Øksendal
Pages 133-154
11. Bernt Øksendal
Pages 155-179
12. Bernt Øksendal
Pages 180-199
13. Back Matter
Pages 200-228

### Introduction

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

### Keywords

Brownian motion Differential Equations Equations Optimal Filtering Stochastic Control Stochastic calculus application applications calculus differential equation filtering theory mathematical finance optimal stopping stoc stochastic analysis

#### Authors and affiliations

• Bernt Øksendal
• 1
1. 1.Department of MathematicsUniversity of OsloOslo 3Norway

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-02847-6
• Copyright Information Springer-Verlag Berlin Heidelberg 1992
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-53335-1
• Online ISBN 978-3-662-02847-6
• Series Print ISSN 0172-5939
• Series Online ISSN 2191-6675