Stochastic Differential Equations and Applications. Volume 1

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

• Publisher: Elsevier Inc, Academic Press
• Year: 1975
• Tongue: English
• Leaves: 238
• Series: Probability & Mathematical Statistics Monograph
• 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:
Front Matter, Page iii
Copyright, Page iv
Preface, Page ix
General Notation, Page xi
Contents of Volume 2, Page xiii
1 - Stochastic Processes, Pages 1-17
2 - Markov Processes, Pages 18-35
3 - Brownian Motion, Pages 36-54
4 - The Stochastic Integral, Pages 55-97
5 - Stochastic Differential Equations, Pages 98-127
6 - Elliptic and Parabolic Partial Differential Equations and Their Relations to Stochastic Differential Equations, Pages 128-151
7 - The Cameron–Martin–Girsanov Theorem, Pages 152-171
8 - Asymptotic Estimates for Solutions, Pages 172-195
9 - Recurrent and Transient Solutions, Pages 196-223
Bibliographical Remarks, Pages 224-225
References, Pages 226-228
Index, Pages 1-3
Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2