Transportation cost inequalities on path and loop groups

DOI10.1016/j.jfa.2004.02.002zbMath1068.60013OpenAlexW2034508498MaRDI QIDQ1763935

Shizan Fang, Jing Hai Shao

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2004.02.002

zbMATH Keywords

path groupWasserstein distanceKullback information

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Talagrand's \(T_2\)-transportation inequality w.r.t. a uniform metric for diffusions, Hamilton-Jacobi semi-groups in infinite dimensional spaces, Optimal transport maps for Monge-Kantorovich problem on loop groups, Concentration for multidimensional diffusions and their boundary local times, Talagrand's \(T_2\)-transportation inequality and log-Sobolev inequality for dissipative SPDEs and applications to reaction-diffusion equations, From the heat measure to the pinned Wiener measure on loop groups, Fokker-Planck equation with respect to heat measures on loop groups, Generalized transportation-cost inequalities and applications, Talagrand inequality on free path space and application to stochastic reaction diffusion equations, Transportation cost inequality for backward stochastic differential equations with mean reflection, An equivalent condition between Poincaré inequality and \(T_{2}\)-transportation cost inequality, Transportation-cost inequality on path spaces with uniform distance, Transportation cost inequalities for SDEs with irregular drifts, Riemannian distance, Rademacher theorem and transportation cost inequality on loop groups., Optimal transport maps on infinite dimensional spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Logarithmic Sobolev inequalities on loop groups
• Logarithmic Sobolev inequalities on Lie groups
• Integration by parts and quasi-invariance for heat kernel measures on loop groups
• Probability distance inequalities on Riemannian manifolds and path spaces.
• Small-time Gaussian behavior of symmetric diffusion semigroups
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Hypercontractivity of Hamilton-Jacobi equations.
• Measure transport on Wiener space and the Girsanov theorem.
• Integration by parts formula and logarithmic Sobolev inequality on the path space over loop groups
• Transportation cost-information inequalities and applications to random dynamical systems and diffusions.
• Transportation cost for Gaussian and other product measures
• Logarithmic Sobolev inequalities for pinned loop groups
• Rademacher's theorem for Wiener functionals
• Measurable metrics and Gaussian concentration