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 Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 2, Pages 387–397 (Mi tvp3929)

Short Communications

Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution

D. A. Korshunov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider the sums $S_n=\xi_1+…+\xi_n$ of independent identically distributed random variables with negative mean value. In the case of subexponential distribution of the summands, the asymptotic behavior is found for the probability of the event that the maximum of sums $\max(S_1,\ldots,S_n)$ exceeds high level $x$. The asymptotics obtained describe this tail probability uniformly with respect to all values of $n$.

Keywords: maxima of sums of random variables, homogeneous Markov chain, large deviation probabilities, subexponential distribution, integrated tail distribution.

DOI: https://doi.org/10.4213/tvp3929

Full text: PDF file (1204 kB)

English version:
Theory of Probability and its Applications, 2002, 46:2, 355–366

Bibliographic databases:

Citation: D. A. Korshunov, “Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 387–397; Theory Probab. Appl., 46:2 (2002), 355–366

Citation in format AMSBIB
\Bibitem{Kor01} \by D.~A.~Korshunov \paper Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution \jour Teor. Veroyatnost. i Primenen. \yr 2001 \vol 46 \issue 2 \pages 387--397 \mathnet{http://mi.mathnet.ru/tvp3929} \crossref{https://doi.org/10.4213/tvp3929} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1968696} \zmath{https://zbmath.org/?q=an:1005.60060} \transl \jour Theory Probab. Appl. \yr 2002 \vol 46 \issue 2 \pages 355--366 \crossref{https://doi.org/10.1137/S0040585X97979019} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000176400600013} 

• http://mi.mathnet.ru/eng/tvp3929
• https://doi.org/10.4213/tvp3929
• http://mi.mathnet.ru/eng/tvp/v46/i2/p387

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Related articles on Google Scholar: Russian articles, English articles

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