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Teor. Veroyatnost. i Primenen., 2012, Volume 57, Issue 4, Pages 701–723 (Mi tvp4475)  

This article is cited in 4 scientific papers (total in 4 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

Abstract: The stability property in Cramérs 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: Cramérs theorem; Cramérs characterization of the normal law; stability problems.

DOI: https://doi.org/10.4213/tvp4475

Full text: PDF file (224 kB)
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English version:
Theory of Probability and its Applications, 2013, 57:4, 568–588

Bibliographic databases:

MSC: 60
Received: 26.04.2011
Language:

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Kontoyiannis, M. Madiman, “Sumset and inverse sumset inequalities for differential entropy and mutual information”, IEEE Trans. Inform. Theory, 60:8 (2014), 4503–4514  crossref  mathscinet  zmath  isi
    2. K. Ball, P. Nayar, T. Tkocz, “A reverse entropy power inequality for log-concave random vectors”, Studia Math., 235:1 (2016), 17–30  crossref  mathscinet  zmath  isi  scopus
    3. F. Feo, E. Indrei, M. R. Posteraro, C. Roberto, “Some remarks on the stability of the log-Sobolev inequality for the Gaussian measure”, Potential Anal., 47:1 (2017), 37–52  crossref  mathscinet  zmath  isi
    4. Bobkov S.G., Chistyakov G.P., Goetze F., “Poincare Inequalities and Normal Approximation For Weighted Sums”, Electron. J. Probab., 25 (2020), 155  crossref  mathscinet  isi
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