A large deviation approach to some transportation cost inequalities

• 成果类型: Article
• 署名作者: Gozlan, Nathael; Leonard, Christian
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0045-y
• 发表日期: 2007
• 页码: 235-283
• 关键词: divergence; THEOREM

摘要

New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Gotze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviations of empirical processes.