Analysis for Diffusion Processes on Riemannian Manifolds

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.

Contents:

• Preliminaries
• Diffusion Processes on Riemannian Manifolds without Boundary
• Reflecting Diffusion Processes on Manifolds with Boundary
• Stochastic Analysis on Path Space over Manifolds with Boundary
• Subelliptic Diffusion Processes

Readership: Graduate students, researchers and professionals in probability theory, differential geometry and partial differential equations.
Key Features:

• First book where the key theory and machinery of the reflecting diffusion processes on Riemannian manifolds with boundary are systematically introduced
• First book to clarify intrinsic links between the semigroup properties on one hand and geometric quantities (curvature and second fundamental form) on the other, and these links are introduced in an easy to understand manner: by formulating geometric quantities using short time behaviors of derivatives of the semigroup, whereby a reader can easily comprehend the equivalence of semigroup properties associated with lower bounds of these geometric quantities
• First book where stochastic analysis on Riemannian manifolds with boundary are introduced