Stochastic Differential Equations

1. Front Matter

   Pages I-XIII

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2. Introduction

   • Bernt Øksendal

   Pages 1-4

3. Some Mathematical Preliminaries

   • Bernt Øksendal

   Pages 5-13

4. Ito Integrals

   • Bernt Øksendal

   Pages 14-31

5. Stochastic Integrals and the Ito Formula

   • Bernt Øksendal

   Pages 32-43

6. Stochastic Differential Equations

   • Bernt Øksendal

   Pages 44-57

7. The Filtering Problem

   • Bernt Øksendal

   Pages 58-85

8. Diffusions: Basic Properties

   • Bernt Øksendal

   Pages 86-104

9. Other Topics in Diffusion Theory

   • Bernt Øksendal

   Pages 105-132

10. Applications to Boundary Value Problems

    • Bernt Øksendal

    Pages 133-154

11. Application to Optimal Stopping

    • Bernt Øksendal

    Pages 155-179

12. Application to Stochastic Control

    • Bernt Øksendal

    Pages 180-199

13. Back Matter

    Pages 200-228

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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

• 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

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

  Bernt Øksendal

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