【摘要】：正A Stein deficit for the logarithmic Sobolev inequality LEDOUX Michel,NOURDIN IvanPECCATI Giovanni Abstract 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.
[Abstract]:Positive A Stein deficit for the logarithmic Sobolev inequality LEDOUX Michel,NOURDIN IvanPECCATI Giovanni Abstract 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.
【分類號(hào)】：Z89

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