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Teoriya Veroyatnostei i ee Primeneniya, 2012, Volume 57, Issue 4, Pages 701–723
DOI: https://doi.org/10.4213/tvp4475 (Mi tvp4475) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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

S. G. Bobkova, G. P. Chistyakovb, F. Götzeb

a University of Minnesota, Department of Mathematics
b Bielefeld University, Department of Mathematics
Full-text PDF (224 kB) Citations (8)
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DOI: https://doi.org/10.4213/tvp4475
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.
Received: 26.04.2011
English version:
Theory of Probability and its Applications, 2013, Volume 57, Issue 4, Pages 568–588
DOI: https://doi.org/10.1137/S0040585X97986217
Bibliographic databases:
Document Type: Article
MSC: 60
Language: English
Citation: 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., 57:4 (2012), 701–723; Theory Probab. Appl., 57:4 (2013), 568–588
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v57/i4/p701
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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