Convergence in Wasserstein Distance for Empirical Measures of Dirichlet Diffusion Processes on Manifolds

2020/05/19 by Wang, Feng-Yu · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.09290

Abstract

Let M be a d-dimensional connected compact Riemannian manifold with boundary ∂ M, let V∈ C²(M) such that μ(\rm d x):=\rm e^V(x)\rm d x is a probability measure, and let X_t be the diffusion process generated by L:=Δ+∇ V with τ:=inf\t≥ 0: X_t∈∂ M\. Consider the empirical measure μ_t:=\frac 1 t ∫₀^t δ_Xs\rm d s under the condition t

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