Probability distance inequalities on Riemannian manifolds and path spaces.

DOI10.1016/S0022-1236(02)00100-3zbMath1048.58013OpenAlexW2103952714MaRDI QIDQ1425155

Feng-Yu Wang

Publication date: 15 March 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-1236(02)00100-3

zbMATH Keywords

entropypath spacefunctional inequalitiescouplingWasserstein distancediffusion semigrouptransportation cost

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Markov semigroups and applications to diffusion processes (47D07) Diffusion processes and stochastic analysis on manifolds (58J65) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

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Cites Work

• Introduction to the theory of (non-symmetric) Dirichlet forms
• Coupling methods for multidimensional diffusion processes
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Formulae for the derivatives of heat semigroups
• Logarithmic Sobolev inequalities and exponential integrability
• Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Hypercontractivity of Hamilton-Jacobi equations.
• A function space large deviation principle for certain stochastic integrals
• Transportation cost for Gaussian and other product measures
• The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications
• On the differentiation of heat semigroups and poisson integrals
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups
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