A new characterization of quadratic transportation-information inequalities

• 成果类型: Article
• 署名作者: Liu, Yuan
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0721-5
• 发表日期: 2017
• 页码: 675-689
• 关键词: cost; lyapunov; SPACES

摘要

It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (LSI for short). The aim of this paper is threefold: (1) To prove the equivalence of and the Lyapunov condition, which gives a new characterization inspired by Cattiaux et al. (Probab Theory Relat Fields 148(1-2):285-304, 2010). (2) To prove the stability of under bounded perturbations, which gives a transference principle in the sense of Holley-Stroock. (3) To prove through a restricted , which gives a counterpart of the restricted LSI presented by Gozlan et al. (Ann Probab 39(3):857-880, 2011).