Wasserstein Convergence for Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds

2022/06/08 by Huaiqian Li, Li, Huaiqian, Bingyao Wu +1 · 1 citation
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2206.03901

openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold M with boundary ∂ M to some reference measure, under the quadratic Wasserstein distance. For any initial distribution not concentrated on ∂ M, we obtain the rate of convergence and even the precise limit for the conditional expectation of the quadratic Wasserstein distance conditioned on the process killed upon exiting M∖∂ M. In particular, the results coincide with the recent ones proved by F.-Y. Wang in \citeeW2 for Dirichlet diffusion processes.

Cited by

• Exact rate of convergence for the empirical measure of a subordinated process in p-Wasserstein distance

Related

• Wasserstein Convergence for Conditional Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds
• Wasserstein Convergence for Empirical Measures of Subordinated Diffusions on Riemannian Manifolds
• Convergence in Wasserstein Distance for Empirical Measures of Dirichlet Diffusion Processes on Manifolds
• Convergence in Wasserstein Distance for Empirical Measures of Non-Symmetric Subordinated Diffusion Processes
• Wasserstein Convergence Rate for Empirical Measures on Noncompact Manifolds