Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law
classification
🧮 math.PR
keywords
characterizationcramerdistributionsentropicnormalregularizedstabilityargument
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For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.
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