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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 1, Pages 62–82 (Mi tvp2155)  

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

Multidimensional integral limit theorems for large deviations

A. K. Aleškevičiene

Vilnius
Abstract: Let $S_n=X^{(1)}+\dots+X^{(n)}$ be a sum of independent identically distributed random vectors in $R^s$ and let $\{D_n\}$, $D_n\subset R^s$, be a sequence of convex Borel sets, for $n=1,2,\dots$. Let the point $a_n$ be the point of $D_n$ which is nearest to the origin. Under general conditions we obtain Cramer's type asymptotical formulas for
$$ \mathbf P\{n^{-1/2}S_n\in D_n\},\qquad|a_n|\ge 1,\qquad|a_n|=o(\sqrt{n}),\qquad n\to\infty. $$
Received: 20.02.1980
English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 1, Pages 65–88
DOI: https://doi.org/10.1137/1128004
Bibliographic databases:
Language: Russian
Citation: A. K. Aleškevičiene, “Multidimensional integral limit theorems for large deviations”, Teor. Veroyatnost. i Primenen., 28:1 (1983), 62–82; Theory Probab. Appl., 28:1 (1984), 65–88
Citation in format AMSBIB
\Bibitem{Ale83}
\by A.~K.~Ale{\v s}kevi{\v{c}}iene
\paper Multidimensional integral limit theorems for large deviations
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 1
\pages 62--82
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=691468}
\zmath{https://zbmath.org/?q=an:0529.60024|0518.60035}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 1
\pages 65--88
\crossref{https://doi.org/10.1137/1128004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SL53600004}
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  • https://www.mathnet.ru/eng/tvp/v28/i1/p62
  • 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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