Stability of Cramer’s Characterization of Normal Laws in Information Distances

Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.

Original languageEnglish (US)
Title of host publicationProgress in Probability
PublisherBirkhauser
Pages3-35
Number of pages33
DOIs
StatePublished - 2016

Publication series

NameProgress in Probability
Volume71
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428

Bibliographical note

Funding Information:
The authors are grateful to the referee for careful reading of the paper and valuable remarks. Bobkov?s research was partially supported by SFB 701 at Bielefeld University, Humboldt Foundation and NSF grant DMS-1612961. Chystyakov and G?tze?s research was partially supported by SFB 701.

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

  • Characterization of normal laws
  • Cramer’s theorem
  • Stability problems

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