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

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3865-3887
Number of pages23
JournalStochastic Processes and their Applications
Volume126
Issue number12
DOIs
StatePublished - Dec 1 2016

Bibliographical note

Funding Information:
This research was partially supported by NSF grant DMS-1612961 , the Humboldt Foundation and SFB 701 at Bielefeld University .

Keywords

  • Cramer's theorem
  • Normal characterization
  • Stability problems

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