| 基于一般Ornstein-Uhlenbeck过程的最优log-Sobolev不等式 |
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| 引用本文： | 李标,商豪.基于一般Ornstein-Uhlenbeck过程的最优log-Sobolev不等式[J].数学杂志,2009,29(2). |
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| 作者姓名： | 李标 商豪 |
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| 作者单位： | 1. 中国人民大学统计学院,北京,100872
2. 湖北工业大学理学院,湖北武汉,430068 |
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| 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.
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| 关 键 词： | log-Sobolev不等式 Ornstein-Uhlenbeck过程 不变测度 Gaussian过程 |
OPTIMAL LOG-SOBOLEV INEQUALITY FOR GENERAL ORNSTEIN-UHLENBECK PROCESSES |
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| LI Biao,SHANG Hao.OPTIMAL LOG-SOBOLEV INEQUALITY FOR GENERAL ORNSTEIN-UHLENBECK PROCESSES[J].Journal of Mathematics,2009,29(2). |
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| Authors: | LI Biao SHANG Hao |
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| Abstract: | 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. |
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| Keywords: | log-Sobolev inequality Ornstein-Uhlenbeck Processes invariant measure Gaussian Processes |
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