Transportation-information inequalities for Markov processes

• 成果类型: Article
• 署名作者: Guillin, Arnaud; Leonard, Christian; Wu, Liming; Yao, Nian
• 署名单位: Aix-Marseille Universite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0159-5
• 发表日期: 2009
• 页码: 669-695
• 关键词: metric measure-spaces; cost; Integrability; CONVERGENCE; deviations; geometry

摘要

chi chi chi In this paper, one investigates the transportation-information TcI inequalities: alpha(T-c(nu, mu)) <= I(nu vertical bar mu) for all probability measures nu on a metric space (X, d), where mu is a given probability measure, T-c(nu, mu) is the transportation cost from nu to mu with respect to the cost function c(x, y) on X-2, I(nu vertical bar mu) is the Fisher-Donsker-Varadhan information of nu with respect to mu and alpha : [0, infinity) -> [0, infinity] is a left continuous increasing function. Using large deviation techniques, it is shown that TcI is equivalent to some concentration inequality for the occupation measure of a mu-reversible ergodic Markov process related to I (center dot vertical bar mu). The tensorization property of TcI and comparisons of TcI with Poincare and log-Sobolev inequalities are investigated. Several easy-to-check sufficient conditions are provided for special important cases of TcI and several examples are worked out.