Precise Limit in Wasserstein Distance for Conditional Empirical Measures of Dirichlet Diffusion Processes

2020/04/16 by Wang, Feng-Yu · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.07537

Abstract

Let M be a d-dimensional connected compact Riemannian manifold with boundary ∂ M, let V∈ C²(M) such that μ(dx):=e^V(x) 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 conditional empirical measure μ_t^ν:= \mathbb E^ν(\frac 1 t ∫₀^t δ_Xsd s|t

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