A Stein deficit for the logarithmic Sobolev inequality

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（7）
• 页码范围: 1163-1180
• 页数: 18页
• 语种: 英文
• DOI: 10.1007/s11425-016-0134-7

摘要

We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution.The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.