Estimates for the Distributions of the Sums of Subexponential Random Variables |
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Authors: | Shneer V. V. |
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Affiliation: | (1) Sobolev Institute of Mathematics, Novosibirsk; Heriot-Watt University, Edinburgh |
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Abstract: | Let be a random walk with independent identically distributed increments . We study the ratios of the probabilities P(Sn>x) / P(1 > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S > x) E P(1 > x) as x . Here is a positive integer-valued random variable independent of . The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process. |
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Keywords: | subexponential distribution distribution with long tail distribution of dominated variation sums of random variables random walk modulated random walk supremum of random walk |
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