Stochastic Differential Equations and Applications: Estimates near infinity5. Relation between K and a diffusion process; 6. The behavior of ξ(t) near S; 7. Existence of a generalized solution in the case of a two-sided obstacle; 8. Existence of a fundame

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. 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. 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 This text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. Originally published in 2 volumes, it combines a book of basic theory with a book of applications. Familiarity with elementary probability is the sole prerequisite. 1975 edition.