Stochastic Differential Equations and Applications

Volume 2

Avner Friedman, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780122682025
• eBook ISBN: 9781483217888
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Stochastic Differential Equations and Applications, Volume 2 is an eight-chapter text that focuses on the practical aspects of stochastic differential equations. This volume begins with a presentation of the auxiliary results in partial differential equations that are needed in the sequel. The succeeding chapters describe the behavior of the sample paths of solutions of stochastic differential equations. These topics are followed by a consideration of an issue whether the paths can hit a given set with positive probability, as well as the stability of paths about a given manifold and with spiraling of paths about this manifold. Other chapters deal with the applications to partial equations, specifically with the Dirichlet problem for degenerate elliptic equations. These chapters also explore the questions of singular perturbations and the existence of fundamental solutions for degenerate parabolic equations. The final chapters discuss stopping time problems, stochastic games, and stochastic differential games. This book is intended primarily to undergraduate and graduate mathematics students.

Table of contents

• Front Cover
• Stochastic Differential Equations and Applications
• Copyright Page
• Table of Contents
• Preface
• General Notation
• Contents of Volume 1
• Chapter 10. Auxiliary Results in Partial Differential Equations
• Chapter 11. Nonattalnability
• Chapter 12. Stability and Spiraling of Solutions
• Chapter 13. The DIrichlet Problem for Degenerate Elliptic Equations
• Chapter 14. Small Random Perturbations of Dynamical Systems
• Chapter 15. Fundamental Solutions for Degenerate Parabolic Equations
• Chapter 16. Stopping Time Problems and Stochastic Games
• Chapter 17. Stochastic Differential Games
• Index