S. G. Bobkov, G. P. Chistyakov, F. Götze, “Stability problems in Cramér-type characterization in case of I.I.D. Summands”, Teor. Veroyatnost. i Primenen., 2012, Volume 57, Issue 4,Pages <nobr>701

This article is cited in 6 papers

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

S. G. Bobkov^a, G. P. Chistyakov^b, F. Götze^b

^a University of Minnesota, Department of Mathematics
^b Bielefeld University, Department of Mathematics

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).

Keywords: Cramér’s theorem; Cramér’s characterization of the normal law; stability problems.

MSC: 60

Received: 26.04.2011

Language: English

DOI: 10.4213/tvp4475