Wasserstein Convergence Rate for Empirical Measures of Markov Chains
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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.
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