Stochastic Differential Equations and Applications. Volume 2

✍ Scribed by Avner Friedman, Z. W. Birnbaum and E. Lukacs (Auth.)

• Publisher: Elsevier Inc, Academic Press
• Year: 1976
• Tongue: English
• Leaves: 308
• Series: Probability & Mathematical Statistics Monographs
• Category: Library

✦ Synopsis

This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.
The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic estimates for solutions. The section concludes with a look at recurrent and transient solutions.
Volume 2 begins with an overview of auxiliary results in partial differential equations, followed by chapters on nonattainability, stability and spiraling of solutions; the Dirichlet problem for degenerate elliptic equations; small random perturbations of dynamical systems; and fundamental solutions of degenerate parabolic equations. Final chapters examine stopping time problems and stochastic games and stochastic differential games. Problems appear at the end of each chapter, and a familiarity with elementary probability is the sole prerequisite.

✦ Table of Contents

Content:
Dedication, Page ii
Front Matter, Page iii
Copyright, Page iv
Preface, Page ix
General Notation, Page xi
Contents of Volume 1, Page xiii
10 - Auxiliary Results in Partial Differential Equations, Pages 229-241
11 - Nonattainability, Pages 242-269
12 - Stability and Spiraling of Solutions, Pages 270-307
13 - The Dirichlet Problem for Degenerate Elliptic Equations, Pages 308-325
14 - Small Random Perturbations of Dynamical Systems, Pages 326-387
15 - Fundamental Solutions for Degenerate Parabolic Equations, Pages 388-432
16 - Stopping Time Problems and Stochastic Games, Pages 433-493
17 - Stochastic Differential Games, Pages 494-519
Bibliographical Remarks, Pages 520-522
References, Pages 523-526
Index, Pages 527-528
Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2