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Stochastic Differential Equations

An Introduction with Applications

  • Textbook
  • © 1989

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 (11 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    • Bernt Øksendal
    Pages 1-4

  3. Some Mathematical Preliminaries

    • Bernt Øksendal
    Pages 5-12

  4. Ito Integrals

    • Bernt Øksendal
    Pages 13-27

  5. Stochastic Integrals and the Ito Formula

    • Bernt Øksendal
    Pages 28-34

  6. Stochastic Differential Equations

    • Bernt Øksendal
    Pages 35-45

  7. The Filtering Problem

    • Bernt Øksendal
    Pages 46-68

  8. Diffusions: Basic Properties

    • Bernt Øksendal
    Pages 69-83

  9. Other Topics in Diffusion Theory

    • Bernt Øksendal
    Pages 84-106

  10. Applications to Boundary Value Problems

    • Bernt Øksendal
    Pages 107-124

  11. Application to Optimal Stopping

    • Bernt Øksendal
    Pages 125-147

  12. Application to Stochastic Control

    • Bernt Øksendal
    Pages 148-163

  13. Back Matter

    Pages 164-188
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About this book

From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. 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 the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book 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." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2

Authors and Affiliations

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

    Bernt Øksendal

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