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The Resource Stochastic analysis on manifolds, Elton P. Hsu

Stochastic analysis on manifolds, Elton P. Hsu

Label
Stochastic analysis on manifolds
Title
Stochastic analysis on manifolds
Statement of responsibility
Elton P. Hsu
Creator
Subject
Language
eng
Cataloging source
DLC
http://library.link/vocab/creatorDate
1959-
http://library.link/vocab/creatorName
Hsu, Elton P.
Dewey number
514/.74
Index
index present
LC call number
QA614.9
LC item number
.H78 2002
Literary form
non fiction
Nature of contents
bibliography
Series statement
Graduate studies in mathematics,
Series volume
v. 38
http://library.link/vocab/subjectName
  • Stochastic differential equations
  • Diffusion processes
  • Geometry, Differential
Label
Stochastic analysis on manifolds, Elton P. Hsu
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 275-278) and index
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 -- 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 -- 8.7. Logarithmic Sobolev inequality on path space
Control code
47254307
Dimensions
26 cm.
Extent
xiv, 281 p.
Isbn
9780821808023
Isbn Type
(acid-free paper)
Lccn
2001046052
Label
Stochastic analysis on manifolds, Elton P. Hsu
Publication
Bibliography note
Includes bibliographical references (p. 275-278) and index
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 -- 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 -- 8.7. Logarithmic Sobolev inequality on path space
Control code
47254307
Dimensions
26 cm.
Extent
xiv, 281 p.
Isbn
9780821808023
Isbn Type
(acid-free paper)
Lccn
2001046052

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