数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2009年
2期
139-142
,共4页
log-Sobolev不等式%Ornstein-Uhlenbeck过程%不变测度%Gaussian过程
log-Sobolev不等式%Ornstein-Uhlenbeck過程%不變測度%Gaussian過程
log-Sobolev불등식%Ornstein-Uhlenbeck과정%불변측도%Gaussian과정
log-Sobolev inequality%Ornstein-Uhlenbeck Processes%invariant measure%Gaussian Processes
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.
本文研究瞭取值于Hilbert空間H且具有唯一不變測度μ的Ornstein-Uhlenbeck過程,利用平穩Gauss過程的log-Sobolev不等式的相關結論,得到瞭該過程滿足log-Sobolev不等式的充分必要條件和最優常數,推廣瞭Gross在對稱情形下的結果.
본문연구료취치우Hilbert공간H차구유유일불변측도μ적Ornstein-Uhlenbeck과정,이용평은Gauss과정적log-Sobolev불등식적상관결론,득도료해과정만족log-Sobolev불등식적충분필요조건화최우상수,추엄료Gross재대칭정형하적결과.
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.
