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Pré-Publication, Document De Travail Année : 2022

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

Résumé

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ 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 $k$-nearest neighbors graph, providing a quantitative answer to a problem of interest to the machine learning community.

Dates et versions

hal-03572834 , version 1 (14-02-2022)

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Thomas Bonis. Stein's method for steady-state diffusion approximation in Wasserstein distance. 2022. ⟨hal-03572834⟩
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