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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 1, Pages 83–97 (Mi tvp2156)  

This article is cited in 5 scientific papers (total in 5 papers)

Central limit theorem for the Banach-valued weakly dependent random variables

V. A. Dmitrovskiĭ, S. V. Ermakov, E. I. Ostrovskiĭ

Obninsk
Full-text PDF (825 kB) Citations (5)
Abstract: Let $B$ be a separable Banach space, $\xi_i$ – a stationary sequence of $B$-valued random variables with zero mean. In this paper we investigate some conditions on the character and rate of mixing under which the sequence $\xi_i$ satisfies the central limit theorem, i. e. the sequence
$$ S_n=n^{-1/2}(\xi_1+\dots+\xi_n),\qquad n\to\infty, $$
converges weakly to some Gaussian $B$-valued variable.
Received: 02.07.1979
English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 1, Pages 89–104
DOI: https://doi.org/10.1137/1128005
Bibliographic databases:
Language: Russian
Citation: V. A. Dmitrovskiǐ, S. V. Ermakov, E. I. Ostrovskiǐ, “Central limit theorem for the Banach-valued weakly dependent random variables”, Teor. Veroyatnost. i Primenen., 28:1 (1983), 83–97; Theory Probab. Appl., 28:1 (1984), 89–104
Citation in format AMSBIB
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\paper Central limit theorem for the Banach-valued weakly dependent random variables
\jour Teor. Veroyatnost. i Primenen.
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\vol 28
\issue 1
\pages 83--97
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=691469}
\zmath{https://zbmath.org/?q=an:0536.60009|0525.60011}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 1
\pages 89--104
\crossref{https://doi.org/10.1137/1128005}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SL53600005}
Linking options:
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  • https://www.mathnet.ru/eng/tvp/v28/i1/p83
  • This publication is cited in the following 5 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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