Stein's method for steady-state diffusion approximation in Wasserstein distance
Probability
2022-03-15 v2
Abstract
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure of a diffusion process and the measure 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 -nearest neighbors graph, providing a quantitative answer to a problem of interest to the machine learning community.
Cite
@article{arxiv.2202.03928,
title = {Stein's method for steady-state diffusion approximation in Wasserstein distance},
author = {Thomas Bonis},
journal= {arXiv preprint arXiv:2202.03928},
year = {2022}
}