Stability problems in cramér-type characterization in case of I.I.D. Summands

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The stability property in Cramér's characterization of the normal law is considered in the case of identically distributed summands. As opposite results, instability is shown with respect to strong distances including the entropic distance to normality (addressing a question of M. Kac).

Original languageEnglish (US)
Pages (from-to)568-588
Number of pages21
JournalTheory of Probability and its Applications
Volume57
Issue number4
DOIs
StatePublished - Nov 12 2013

Keywords

  • Cramér's characterization of the normal law
  • Cramér's theorem
  • Stability problems

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