English

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 μ\mu of a diffusion process and the measure ν\nu 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 kk-nearest neighbors graph, providing a quantitative answer to a problem of interest to the machine learning community.

Keywords

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}
}
R2 v1 2026-06-24T09:26:28.903Z