Stochastic differential equations and applications

Avner Friedman9780122682018, 0122682017

This volume begins with auxiliary results in partial differential equations (Chapter 10) that are needed in the sequel. In Chapters 11 and 12 we study the behavior of the sample paths of solutions of stochastic differential equations in the same spirit as in Chapter 9. Chapter 11 deals with the question whether the paths can hit a given set with positive probability. Chapter 12 is concerned with the stability of paths about a given manifold, and (in case of two dimensions) with spiraling of paths about this manifold. Chapters 13-15 are concerned with applications to partial differential equations. In Chapter 13 we deal with the Dirichlet problem for degenerate elliptic equations. The results of Chapter 12 play here a fundamental role. In Chapter 14 we consider questions of singular perturbations. Chapter 15 is concerned with the existence of fundamental solutions for degenerate parabolic equations. Chapters 16 and 17 deal with stopping time problems, stochastic games and stochastic differential games.