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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 2, Pages 382–390
DOI: https://doi.org/10.4213/tvp116 (Mi tvp116) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the central limit Newman theorem

A. P. Shashkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/tvp116
Abstract: We construct an example of a strictly stationary associated random sequence which does not satisfy the central limit theorem and whose the partial sums' variance grows in a defined regular way. This result generalizes the well-known example of N. Herrndorf and shows the optimality of conditions in the classical Newman's theorem.
Keywords: associated random variables, stationarity, central limit theorem, slowly varying functions.
Received: 14.07.2003
Revised: 25.03.2004
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 2, Pages 330–337
DOI: https://doi.org/10.1137/S0040585X97981731
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. P. Shashkin, “On the central limit Newman theorem”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 382–390; Theory Probab. Appl., 50:2 (2006), 330–337
Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp116
  • https://www.mathnet.ru/eng/tvp/v50/i2/p382
    • This publication is cited in the following 2 articles:
    1. Alexander Bulinski, Evgeny Spodarev, “Central limit theorems for weakly dependent random fields”, Lect. Notes Math., 2068 (2013), 337–383  mathnet  crossref
    2. A. V. Bulinski, “Central limit theorem for positively associated stationary random fields”, Vestnik St.Petersb. Univ.Math., 44:2 (2011), 89  crossref
    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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