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Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang
| Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang |
| Autore | Wang Feng-Yu |
| Pubbl/distr/stampa | Singapore : , : World Scientific Publishing, , 2014 |
| Descrizione fisica | 1 online resource (392 p.) |
| Disciplina | 516.373 |
| Collana | Advanced Series on Statistical Science & Applied Probability |
| Soggetto topico |
Riemannian manifolds
Diffusion processes |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4452-65-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries; 1.1 Riemannian manifold; 1.1.1 Differentiable manifold; 1.1.2 Riemannian manifold; 1.1.3 Some formulae and comparison results; 1.2 Riemannian manifold with boundary; 1.3 Coupling and applications; 1.3.1 Transport problem and Wasserstein distance; 1.3.2 Optimal coupling and optimal map; 1.3.3 Coupling for stochastic processes; 1.3.4 Coupling by change of measure; 1.4 Harnack inequalities and applications; 1.4.1 Harnack inequality; 1.4.2 Shift Harnack inequality; 1.5 Harnack inequality and derivative estimate
1.5.1 Harnack inequality and entropy-gradient estimate1.5.2 Harnack inequality and L2-gradient estimate; 1.5.3 Harnack inequalities and gradient-gradient estimates; 1.6 Functional inequalities and applications; 1.6.1 Poincar e type inequality and essential spectrum; 1.6.2 Exponential decay in the tail norm; 1.6.3 The F-Sobolev inequality; 1.6.4 Weak Poincare inequality; 1.6.5 Equivalence of irreducibility and weak Poincare inequality; 2. Diffusion Processes on Riemannian Manifolds without Boundary; 2.1 Brownian motion with drift; 2.2 Formulae for Pt and RicZ 2.3 Equivalent semigroup inequalities for curvature lower bound2.4 Applications of equivalent semigroup inequalities; 2.5 Transportation-cost inequality; 2.5.1 From super Poincare to weighted log-Sobolev inequalities; 2.5.2 From log-Sobolev to transportation-cost inequalities; 2.5.3 From super Poincare to transportation-cost inequalities; 2.5.4 Super Poincare inequality by perturbations; 2.6 Log-Sobolev inequality: Different roles of Ric and Hess; 2.6.1 Exponential estimate and concentration of; 2.6.2 Harnack inequality and the log-Sobolev inequality 2.6.3 Hypercontractivity and ultracontractivity2.7 Curvature-dimension condition and applications; 2.7.1 Gradient and Harnack inequalities; 2.7.2 HWI inequalities; 2.8 Intrinsic ultracontractivity on non-compact manifolds; 2.8.1 The intrinsic super Poincare inequality; 2.8.2 Curvature conditions for intrinsic ultracontractivity; 2.8.3 Some examples; 3. Reflecting Diffusion Processes on Manifolds with Boundary; 3.1 Kolmogorov equations and the Neumann problem; 3.2 Formulae for Pt, RicZ and I; 3.2.1 Formula for Pt; 3.2.2 Formulae for RicZ and I; 3.2.3 Gradient estimates 3.3 Equivalent semigroup inequalities for curvature conditionand lower bound of I3.3.1 Equivalent statements for lower bounds of RicZ and I; 3.3.2 Equivalent inequalities for curvature-dimension condition and lower bound of I; 3.4 Harnack inequalities for SDEs on Rd and extension to nonconvex manifolds; 3.4.1 Construction of the coupling; 3.4.2 Harnack inequality on Rd; 3.4.3 Extension to manifolds with convex boundary; 3.4.4 Neumann semigroup on non-convex manifolds; 3.5 Functional inequalities; 3.5.1 Estimates for inequality constants on compact manifolds 3.5.2 A counterexample for Bakry-Emery criterion |
| Record Nr. | UNINA-9910453237703321 |
Wang Feng-Yu
|
||
| Singapore : , : World Scientific Publishing, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang, Beijing Normal University, China & Swansea University, UK
| Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang, Beijing Normal University, China & Swansea University, UK |
| Autore | Wang Feng-Yu |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xii, 379 pages) : illustrations |
| Disciplina | 516.373 |
| Collana | Advanced Series on Statistical Science & Applied Probability |
| Soggetto topico |
Riemannian manifolds
Diffusion processes |
| ISBN | 981-4452-65-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries; 1.1 Riemannian manifold; 1.1.1 Differentiable manifold; 1.1.2 Riemannian manifold; 1.1.3 Some formulae and comparison results; 1.2 Riemannian manifold with boundary; 1.3 Coupling and applications; 1.3.1 Transport problem and Wasserstein distance; 1.3.2 Optimal coupling and optimal map; 1.3.3 Coupling for stochastic processes; 1.3.4 Coupling by change of measure; 1.4 Harnack inequalities and applications; 1.4.1 Harnack inequality; 1.4.2 Shift Harnack inequality; 1.5 Harnack inequality and derivative estimate
1.5.1 Harnack inequality and entropy-gradient estimate1.5.2 Harnack inequality and L2-gradient estimate; 1.5.3 Harnack inequalities and gradient-gradient estimates; 1.6 Functional inequalities and applications; 1.6.1 Poincar e type inequality and essential spectrum; 1.6.2 Exponential decay in the tail norm; 1.6.3 The F-Sobolev inequality; 1.6.4 Weak Poincare inequality; 1.6.5 Equivalence of irreducibility and weak Poincare inequality; 2. Diffusion Processes on Riemannian Manifolds without Boundary; 2.1 Brownian motion with drift; 2.2 Formulae for Pt and RicZ 2.3 Equivalent semigroup inequalities for curvature lower bound2.4 Applications of equivalent semigroup inequalities; 2.5 Transportation-cost inequality; 2.5.1 From super Poincare to weighted log-Sobolev inequalities; 2.5.2 From log-Sobolev to transportation-cost inequalities; 2.5.3 From super Poincare to transportation-cost inequalities; 2.5.4 Super Poincare inequality by perturbations; 2.6 Log-Sobolev inequality: Different roles of Ric and Hess; 2.6.1 Exponential estimate and concentration of; 2.6.2 Harnack inequality and the log-Sobolev inequality 2.6.3 Hypercontractivity and ultracontractivity2.7 Curvature-dimension condition and applications; 2.7.1 Gradient and Harnack inequalities; 2.7.2 HWI inequalities; 2.8 Intrinsic ultracontractivity on non-compact manifolds; 2.8.1 The intrinsic super Poincare inequality; 2.8.2 Curvature conditions for intrinsic ultracontractivity; 2.8.3 Some examples; 3. Reflecting Diffusion Processes on Manifolds with Boundary; 3.1 Kolmogorov equations and the Neumann problem; 3.2 Formulae for Pt, RicZ and I; 3.2.1 Formula for Pt; 3.2.2 Formulae for RicZ and I; 3.2.3 Gradient estimates 3.3 Equivalent semigroup inequalities for curvature conditionand lower bound of I3.3.1 Equivalent statements for lower bounds of RicZ and I; 3.3.2 Equivalent inequalities for curvature-dimension condition and lower bound of I; 3.4 Harnack inequalities for SDEs on Rd and extension to nonconvex manifolds; 3.4.1 Construction of the coupling; 3.4.2 Harnack inequality on Rd; 3.4.3 Extension to manifolds with convex boundary; 3.4.4 Neumann semigroup on non-convex manifolds; 3.5 Functional inequalities; 3.5.1 Estimates for inequality constants on compact manifolds 3.5.2 A counterexample for Bakry-Emery criterion |
| Record Nr. | UNINA-9910790868003321 |
|
Wang Feng-Yu
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang, Beijing Normal University, China & Swansea University, UK
| Analysis for diffusion processes on Riemannian manifolds / / Feng-Yu Wang, Beijing Normal University, China & Swansea University, UK |
| Autore | Wang Feng-Yu |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xii, 379 pages) : illustrations |
| Disciplina | 516.373 |
| Collana | Advanced Series on Statistical Science & Applied Probability |
| Soggetto topico |
Riemannian manifolds
Diffusion processes |
| ISBN | 981-4452-65-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries; 1.1 Riemannian manifold; 1.1.1 Differentiable manifold; 1.1.2 Riemannian manifold; 1.1.3 Some formulae and comparison results; 1.2 Riemannian manifold with boundary; 1.3 Coupling and applications; 1.3.1 Transport problem and Wasserstein distance; 1.3.2 Optimal coupling and optimal map; 1.3.3 Coupling for stochastic processes; 1.3.4 Coupling by change of measure; 1.4 Harnack inequalities and applications; 1.4.1 Harnack inequality; 1.4.2 Shift Harnack inequality; 1.5 Harnack inequality and derivative estimate
1.5.1 Harnack inequality and entropy-gradient estimate1.5.2 Harnack inequality and L2-gradient estimate; 1.5.3 Harnack inequalities and gradient-gradient estimates; 1.6 Functional inequalities and applications; 1.6.1 Poincar e type inequality and essential spectrum; 1.6.2 Exponential decay in the tail norm; 1.6.3 The F-Sobolev inequality; 1.6.4 Weak Poincare inequality; 1.6.5 Equivalence of irreducibility and weak Poincare inequality; 2. Diffusion Processes on Riemannian Manifolds without Boundary; 2.1 Brownian motion with drift; 2.2 Formulae for Pt and RicZ 2.3 Equivalent semigroup inequalities for curvature lower bound2.4 Applications of equivalent semigroup inequalities; 2.5 Transportation-cost inequality; 2.5.1 From super Poincare to weighted log-Sobolev inequalities; 2.5.2 From log-Sobolev to transportation-cost inequalities; 2.5.3 From super Poincare to transportation-cost inequalities; 2.5.4 Super Poincare inequality by perturbations; 2.6 Log-Sobolev inequality: Different roles of Ric and Hess; 2.6.1 Exponential estimate and concentration of; 2.6.2 Harnack inequality and the log-Sobolev inequality 2.6.3 Hypercontractivity and ultracontractivity2.7 Curvature-dimension condition and applications; 2.7.1 Gradient and Harnack inequalities; 2.7.2 HWI inequalities; 2.8 Intrinsic ultracontractivity on non-compact manifolds; 2.8.1 The intrinsic super Poincare inequality; 2.8.2 Curvature conditions for intrinsic ultracontractivity; 2.8.3 Some examples; 3. Reflecting Diffusion Processes on Manifolds with Boundary; 3.1 Kolmogorov equations and the Neumann problem; 3.2 Formulae for Pt, RicZ and I; 3.2.1 Formula for Pt; 3.2.2 Formulae for RicZ and I; 3.2.3 Gradient estimates 3.3 Equivalent semigroup inequalities for curvature conditionand lower bound of I3.3.1 Equivalent statements for lower bounds of RicZ and I; 3.3.2 Equivalent inequalities for curvature-dimension condition and lower bound of I; 3.4 Harnack inequalities for SDEs on Rd and extension to nonconvex manifolds; 3.4.1 Construction of the coupling; 3.4.2 Harnack inequality on Rd; 3.4.3 Extension to manifolds with convex boundary; 3.4.4 Neumann semigroup on non-convex manifolds; 3.5 Functional inequalities; 3.5.1 Estimates for inequality constants on compact manifolds 3.5.2 A counterexample for Bakry-Emery criterion |
| Record Nr. | UNINA-9910806814403321 |
|
Wang Feng-Yu
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Harnack inequalities for stochastic partial differential equations / / Feng-Yu Wang
| Harnack inequalities for stochastic partial differential equations / / Feng-Yu Wang |
| Autore | Wang Feng-Yu |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York, : Springer, c2013 |
| Descrizione fisica | 1 online resource (x, 125 pages) |
| Disciplina | 515.353 |
| Collana | SpringerBriefs in mathematics |
| Soggetto topico |
Differential equations
Mathematical analysis |
| ISBN | 1-4614-7934-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Preface""; ""Contents""; ""Chapter 1 A General Theory of Dimension-Free Harnack Inequalities""; ""1.1 Coupling by Change of Measure and Applications""; ""1.1.1 Harnack Inequalities and Bismut Derivative Formulas""; ""1.1.2 Shift Harnack Inequalities and Integration by PartsFormulas""; ""1.2 Derivative Formulas Using the Malliavin Calculus""; ""1.2.1 Bismut Formulas""; ""1.2.2 Integration by Parts Formulas""; ""1.3 Harnack Inequalities and Gradient Inequalities""; ""1.3.1 Gradient�Entropy and Harnack Inequalities""; ""1.3.2 From Gradient�Gradient to Harnack Inequalities""
""1.3.3 L2 Gradient and Harnack Inequalities""""1.4 Applications of Harnack and Shift Harnack Inequalities""; ""1.4.1 Applications of the Harnack Inequality""; ""1.4.2 Applications of the Shift Harnack Inequality""; ""Chapter 2 Nonlinear Monotone Stochastic Partial Differential Equations""; ""2.1 Solutions of Monotone Stochastic Equations""; ""2.2 Harnack Inequalities for 1""; ""2.3 Harnack Inequalities for (0,1)""; ""2.4 Applications to Specific Models ""; ""2.4.1 Stochastic Generalized Porous Media Equations""; ""2.4.2 Stochastic p-Laplacian Equations"" ""2.4.3 Stochastic Generalized Fast-Diffusion Equations""""Chapter 3 Semilinear Stochastic Partial Differential Equations""; ""3.1 Mild Solutions and Finite-Dimensional Approximations""; ""3.2 Additive Noise""; ""3.2.1 Harnack Inequalities and Bismut Formula""; ""3.2.2 Shift Harnack Inequalities and Integration by PartsFormula""; ""3.3 Multiplicative Noise: The Log-Harnack Inequality""; ""3.3.1 The Main Result""; ""3.3.2 Application to White-Noise-Driven SPDEs""; ""3.4 Multiplicative Noise: Harnack Inequality with Power""; ""3.4.1 Construction of the Coupling"" ""3.4.2 Proof of Theorem 3.4.1""""3.5 Multiplicative Noise: Bismut Formula""; ""Chapter 4 Stochastic Functional (Partial) Differential Equations""; ""4.1 Solutions and Finite-Dimensional Approximations""; ""4.1.1 Stochastic Functional Differential Equations""; ""4.1.2 Semilinear Stochastic Functional Partial Differential Equations""; ""4.2 Elliptic Stochastic Functional Partial Differential Equations with Additive Noise""; ""4.2.1 Harnack Inequalities and Bismut Formula""; ""4.2.2 Shift Harnack Inequalities and Integration by PartsFormulas""; ""4.2.3 Extensions to Semilinear SDPDEs"" ""4.3 Elliptic Stochastic Functional Partial Differential Equations with Multiplicative Noise""""4.3.1 Log-Harnack Inequality""; ""4.3.1.1 Proofs of (i)""; ""4.3.1.2 Proof of (ii)""; ""4.3.1.3 Proof of (iii)""; ""4.3.2 Harnack Inequality with Power""; ""4.3.3 Bismut Formulas for Semilinear SDPDEs""; ""4.4 Stochastic Functional Hamiltonian System""; ""4.4.1 Main Result and Consequences""; ""4.4.2 Proof of Theorem 4.4.1""; ""4.4.3 Proofs of Corollary 4.4.3 and Theorem 4.4.5 ""; ""Glossary""; ""References""; ""Index"" |
| Record Nr. | UNINA-9910438028703321 |
|
Wang Feng-Yu
|
||
| New York, : Springer, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||