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catalog contributor b12404170.
catalog created "c2002.".
catalog date "2002".
catalog date "c2002.".
catalog dateCopyrighted "c2002.".
catalog description "5.3. Short-time asymptotics: distant points -- 5.4. Brownian bridge -- 5.5. Derivatives of the logarithmic heat kernel -- Ch. 6. Further Applications -- 6.1. Dirichlet problem at infinity -- 6.2. Constant upper bound -- 6.3. Vanishing upper bound -- 6.4. Radially symmetric manifolds -- 6.5. Coupling of Brownian motion -- 6.6. Coupling and index form -- 6.7. Eigenvalue estimates -- Ch. 7. Brownian Motion and Index Theorems -- 7.1. Weitzenbock formula -- 7.2. Heat equation on differential forms -- 7.3. Gauss-Bonnet-Chern formula -- 7.4. Clifford algebra and spin group -- 7.5. Spin bundle and the Dirac operator -- 7.6. Atiyah-Singer index theorem -- 7.7. Brownian holonomy -- Ch. 8. Analysis on Path Spaces -- 8.1. Quasi-invariance of the Wiener measure -- 8.2. Flat path space -- 8.3. Gradient formulas -- 8.4. Integration by parts in path space -- 8.5. Martingale representation theorem -- 8.6. Logarithmic Sobolev inequality and hypercontractivity -- ".
catalog description "8.7. Logarithmic Sobolev inequality on path space.".
catalog description "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 -- ".
catalog description "Includes bibliographical references (p. 275-278) and index.".
catalog extent "xiv, 281 p. ;".
catalog identifier "0821808028 (acid-free paper)".
catalog isPartOf "Graduate studies in mathematics, 1065-7339 ; v. 38".
catalog issued "2002".
catalog issued "c2002.".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog subject "514/.74 21".
catalog subject "Diffusion processes.".
catalog subject "Geometry, Differential.".
catalog subject "QA614.9 .H78 2002".
catalog subject "Stochastic differential equations.".
catalog tableOfContents "5.3. Short-time asymptotics: distant points -- 5.4. Brownian bridge -- 5.5. Derivatives of the logarithmic heat kernel -- Ch. 6. Further Applications -- 6.1. Dirichlet problem at infinity -- 6.2. Constant upper bound -- 6.3. Vanishing upper bound -- 6.4. Radially symmetric manifolds -- 6.5. Coupling of Brownian motion -- 6.6. Coupling and index form -- 6.7. Eigenvalue estimates -- Ch. 7. Brownian Motion and Index Theorems -- 7.1. Weitzenbock formula -- 7.2. Heat equation on differential forms -- 7.3. Gauss-Bonnet-Chern formula -- 7.4. Clifford algebra and spin group -- 7.5. Spin bundle and the Dirac operator -- 7.6. Atiyah-Singer index theorem -- 7.7. Brownian holonomy -- Ch. 8. Analysis on Path Spaces -- 8.1. Quasi-invariance of the Wiener measure -- 8.2. Flat path space -- 8.3. Gradient formulas -- 8.4. Integration by parts in path space -- 8.5. Martingale representation theorem -- 8.6. Logarithmic Sobolev inequality and hypercontractivity -- ".
catalog tableOfContents "8.7. Logarithmic Sobolev inequality on path space.".
catalog tableOfContents "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 -- ".
catalog title "Stochastic analysis on manifolds / Elton P. Hsu.".
catalog type "text".