Stein's method for steady-state diffusion approximation in Wasserstein distance

2022/02/08 by Bonis, Thomas
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.03928

Abstract

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure μ of a diffusion process and the measure ν of an approximating Markov chain. Our result is obtained thanks to a generalization of a new approach to Stein's method which may be of independent interest. As an application, we study the invariant measure of a random walk on a k-nearest neighbors graph, providing a quantitative answer to a problem of interest to the machine learning community.

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