E-raamat: Analysis for Diffusion Processes on Riemannian Manifolds [World Scientific e-raamat]

Drawing on and complementing published literature since the turn of the century, Wang presents a self-contained theory concerning diffusion processes on Riemannian manifolds with or without boundary. He begins by setting out fundamental results from Riemannian manifolds, coupling method and applications, and a brief theory of functional inequalities. Then he discusses diffusion processes on Riemannian manifolds without boundary, reflecting diffusion processes on manifolds with boundary, stochastic analysis on path space over manifolds with boundary, and sub-elliptic diffusion processes. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.