Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 162, Issue 3-4, Pages 707-738Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-014-0583-7
Keywords
Empirical measure; Sequence of i.i.d. random variables; Wasserstein distance; Concentration inequalities; Quantization; Markov chains; rho-mixing sequences; Mc Kean-Vlasov particles system
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Let be the empirical measure associated to a -sample of a given probability distribution on . We are interested in the rate of convergence of to , when measured in the Wasserstein distance of order . We provide some satisfying non-asymptotic -bounds and concentration inequalities, for any values of and . We extend also the non asymptotic -bounds to stationary -mixing sequences, Markov chains, and to some interacting particle systems.
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