# Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance

@article{Boissard2011SimpleBF,
title={Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance},
author={Emmanuel Boissard},
journal={Electronic Journal of Probability},
year={2011},
volume={16},
pages={2296-2333}
}
• Emmanuel Boissard
• Published 2011
• Mathematics
• Electronic Journal of Probability
• We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting… CONTINUE READING
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