On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

Details On the mean speed of convergence of empirical and occupation measures in Wasserstein distance On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

2011-05-26

arxiv.org/abs/1105.5263v1

Mathematics

Probability

Scientific paper

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably highlighted in the example of infinite-dimensional Gaussian measures.

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