Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels

2020/10/27 by Max Fathi, Dan Mikulincer, Fathi, Max +1 · 3 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2010.14178

Abstract

We investigate stability of invariant measures of diffusion processes with respect to L^p distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to study transport equations. As an application, we prove a partial extension of an inequality of Ledoux, Nourdin and Peccati relating transport distances and Stein discrepancies to a non-Gaussian setting via the moment map construction of Stein kernels.

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