基于一般Ornstein-Uhlenbeck过程的最优log-Sobolev不等式

摘要

本文研究了取值于Hilbert空间H且具有唯一不变测度μ的Ornstein-Uhlenbeck过程,利用平稳Gauss过程的log-Sobolev不等式的相关结论,得到了该过程满足log-Sobolev不等式的充分必要条件和最优常数,推广了Gross在对称情形下的结果.%In this paper ,we mainly discuss the general Ornstein-Uhlenbeck processes valued in a Hilbert space with the unique invariant measure.With the results in log-Sobolev inequality for general Gaussian processes, we obtain the necessary and sufficient condition for the log-Sobolev inequality and provide the best constant, which extend Gross' result in symmetry situation.