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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 382–390 (Mi tvp116)  

Short Communications

On the central limit Newman theorem

A. P. Shashkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/tvp116

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English version:
Theory of Probability and its Applications, 2006, 50:2, 330–337

Bibliographic databases:

Received: 14.07.2003
Revised: 25.03.2004

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

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