On the rate of convergence in Wasserstein distance of the empirical measure

• 成果类型: Article
• 署名作者: Fournier, Nicolas; Guillin, Arnaud
• 署名单位: Sorbonne Universite; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0583-7
• 发表日期: 2015
• 页码: 707-738
• 关键词: granular media equations; transportation-cost; inequalities; sums

摘要

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.