Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law

S. G. Bobkov; G. P. Chistyakov; F. Götze

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arXiv · 1504.02961

Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law

S. G. Bobkov·G. P. Chistyakov·F. Götze

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Abstract

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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S. G. Bobkov, G. P. Chistyakov, F. Götze. 2015-04-12. Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law. https://arxiv.org/abs/1504.02961

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