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This article is cited in 62 scientific papers (total in 62 papers)
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 $S_n=\xi_1+\dots+\xi_n$ 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.
Received: 19.10.1998
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
Linking options:
https://www.mathnet.ru/eng/tvp3929https://doi.org/10.4213/tvp3929 https://www.mathnet.ru/eng/tvp/v46/i2/p387
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