Wasserstein Convergence Rate for Empirical Measures of Markov Chains

01/18/2021

∙

by   Adrian Riekert, et al.

∙

0

∙

share

We consider a Markov chain on ℝ^d with invariant measure μ. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to the 1-Wasserstein distance. The main result of this article is a new upper bound for the expected Wasserstein distance, which is proved by combining the Kantorovich dual formula with a Fourier expansion. In addition, we show how concentration inequalities around the mean can be obtained.