Wasserstein convergence rate for empirical measures on noncompact manifolds

DOI10.1016/j.spa.2021.11.006zbMath1480.58015arXiv2007.14667OpenAlexW3215689420MaRDI QIDQ2066968

Yanyan Li

Publication date: 17 January 2022

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.14667

zbMATH Keywords

Riemannian manifolddiffusion processempirical measureWasserstein distance

Mathematics Subject Classification ID

Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65) Convergence of probability measures (60B10)

Related Items (8)

Convergence in Wasserstein distance for empirical measures of Dirichlet diffusion processes on manifolds ⋮ Wasserstein convergence for empirical measures of subordinated diffusions on Riemannian manifolds ⋮ Empirical approximation to invariant measures for McKean-Vlasov processes: mean-field interaction vs self-interaction ⋮ Convergence in Wasserstein distance for empirical measures of semilinear SPDEs ⋮ Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds ⋮ Wasserstein convergence rates for empirical measures of subordinated processes on noncompact manifolds ⋮ Precise limit in Wasserstein distance for conditional empirical measures of Dirichlet diffusion processes ⋮ Wasserstein asymptotics for the empirical measure of fractional Brownian motion on a flat torus

Cites Work

• Unnamed Item
• Unnamed Item
• Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds
• The radial part of Brownian motion on a manifold: A semimartingale property
• Existence of the spectral gap for elliptic operators
• A PDE approach to a 2-dimensional matching problem
• Precise limit in Wasserstein distance for conditional empirical measures of Dirichlet diffusion processes
• Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds
• Heat Kernel Estimates with Application to Compactness of Manifolds
• Analysis for Diffusion Processes on Riemannian Manifolds
• Central limit theorems for additive functionals of ergodic Markov diffusions processes
• Approximation by finitely supported measures
• FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES
• Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
• Harnack Inequalities for Stochastic Partial Differential Equations

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