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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 4, Pages 785–793
DOI: https://doi.org/10.4213/tvp26 (Mi tvp26) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Precise estimates of the metric entropy for the set of arithmetic averages of quasi-stationary processes

V. F. Gaposhkin

Moscow State University of Railway Communications
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DOI: https://doi.org/10.4213/tvp26
Abstract: Estimates of the $\varepsilon$-entropy of the set of arithmetic averages for an $R$-quasi-stationary system are obtained depending on the decay rate of the function $R(n)$. It is shown that the deduced estimates are the best in order as $\varepsilon\to+0$.
Keywords: stationary and quasi-stationary sequences, $R$-systems, arithmetic average, $\varepsilon$-entropy of the sets of arithmetic averages, upper and lower estimates.
Received: 15.06.2005
Revised: 15.05.2006
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 4, Pages 695–704
DOI: https://doi.org/10.1137/S0040585X97982724
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. F. Gaposhkin, “Precise estimates of the metric entropy for the set of arithmetic averages of quasi-stationary processes”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 785–793; Theory Probab. Appl., 51:4 (2007), 695–704
Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp26
  • https://www.mathnet.ru/eng/tvp/v51/i4/p785
    • This publication is cited in the following 1 articles:
    1. V. F. Gaposhkin, “Exact Estimates of the Metric Entropy of the Averages for Some Classes of Stationary Sequences”, Theory Probab. Appl., 53:1 (2009), 37–58  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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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    Abstract page:349
    Full-text PDF :193
    References:75
    First page:17
     
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