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Teoriya Veroyatnostei i ee Primeneniya, 1982, Volume 27, Issue 2, Pages 337–339 (Mi tvp2354)  
This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

Central limit theorem for stationary sequences in the Hilbert space

V. V. Mal'cev, E. I. Ostrovskiĭ

Obninsk
Full-text PDF (228 kB) Citations (5)
Abstract: Let $\xi_i$ be a centered strong stationary sequence in the separable Hilbert space $H$. We say that $\xi_i$ satisfy CLT if $S_n=n^{-1/2}(\xi_1+\dots+\xi_n)$ converges weakly to a Gaussian variable $\eta$, $\mathbf P\{\eta\in H\}=1$. We study some conditions on a mixing of a sequence $\xi_i$ for this sequence to satisfy CLT.
Received: 04.07.1979
English version:
Theory of Probability and its Applications, 1983, Volume 27, Issue 2, Pages 357–359
DOI: https://doi.org/10.1137/1127036
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Mal'cev, E. I. Ostrovskiǐ, “Central limit theorem for stationary sequences in the Hilbert space”, Teor. Veroyatnost. i Primenen., 27:2 (1982), 337–339; Theory Probab. Appl., 27:2 (1983), 357–359
Citation in format AMSBIB
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\by V.~V.~Mal'cev, E.~I.~Ostrovski{\v\i}
\paper Central limit theorem for stationary sequences in the Hilbert space
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 2
\pages 337--339
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\zmath{https://zbmath.org/?q=an:0505.60014|0493.60008}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 2
\pages 357--359
\crossref{https://doi.org/10.1137/1127036}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1983QN71900012}
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  • https://www.mathnet.ru/eng/tvp/v27/i2/p337
    • 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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