Title: Stochastic analysis on manifolds /
Authors: Hsu, Elton P., 1959-
Publisher: American Mathematical Society,
Year: 2002
Subjects: Stochastic differential equations.; Diffusion processes.; Geometry, Differential.; Geometry, Differential.
Contents: Ch. 1. Stochastic Differential Equations and Diffusions -- 1.1. SDE on euclidean space -- 1.2. SDE on manifolds -- 1.3. Diffusion processes -- Ch. 2. Basic Stochastic Differential Geometry -- 2.1. Frame bundle and connection -- 2.2. Tensor fields -- 2.3. Horizontal lift and stochastic development -- 2.4. Stochastic line integrals -- 2.5. Martingales on manifolds -- 2.6. Martingales on submanifolds -- Ch. 3. Brownian Motion on Manifolds -- 3.1. Laplace-Beltrami operator -- 3.2. Brownian motion on manifolds -- 3.3. Examples of Brownian motion -- 3.4. Distance function -- 3.5. Radial process -- 3.6. An exit time estimate -- Ch. 4. Brownian Motion and Heat Semigroup -- 4.1. Heat kernel as transition density function -- 4.2. Stochastic completeness -- 4.3. C[subscript 0]-property of the heat semigroup -- 4.4. Recurrence and transience -- 4.5. Comparison of heat kernels -- Ch. 5. Short-time Asymptotics -- 5.1. Short-time asymptotics: near points -- 5.2. Varadhan's asymptotic relation --^