Regularized distributions and entropic stability of Cramer's characterization of the normal law

Bobkov SG, Chistyakov GP, Götze F. Regularized distributions and entropic stability of Cramer's characterization of the normal law. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2016;126(12):3865-3887.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. (C) 2016 Elsevier B.V. All rights reserved