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

@article{Boissard2011OnTM,
  title={On the mean speed of convergence of empirical and occupation measures in Wasserstein distance},
  author={Emmanuel Boissard and Thibaut Le Gouic},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  year={2011},
  volume={50},
  pages={539-563}
}
  • Emmanuel Boissard, Thibaut Le Gouic
  • Published 2011
  • Mathematics
  • Annales De L Institut Henri Poincare-probabilites Et Statistiques
  • 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… CONTINUE READING
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