Stochastic Differential Equations: An Introduction with Applications

✍ Scribed by Bernt Øksendal (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 1989
• Tongue: English
• Leaves: 199
• Series: Universitext
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages I-XV
Introduction....Pages 1-4
Some Mathematical Preliminaries....Pages 5-12
Ito Integrals....Pages 13-27
Stochastic Integrals and the Ito Formula....Pages 28-34
Stochastic Differential Equations....Pages 35-45
The Filtering Problem....Pages 46-68
Diffusions: Basic Properties....Pages 69-83
Other Topics in Diffusion Theory....Pages 84-106
Applications to Boundary Value Problems....Pages 107-124
Application to Optimal Stopping....Pages 125-147
Application to Stochastic Control....Pages 148-163
Back Matter....Pages 164-188

✦ Subjects

Probability Theory and Stochastic Processes;Mathematical Methods in Physics;Numerical and Computational Physics;Appl.Mathematics/Computational Methods of Engineering