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 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. 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.