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May 2008 On lower limits and equivalences for distribution tails of randomly stopped sums
Denis Denisov, Serguei Foss, Dmitry Korshunov
Bernoulli 14(2): 391-404 (May 2008). DOI: 10.3150/07-BEJ111

Abstract

For a distribution $F^{*τ}$ of a random sum $S_τ=ξ_1+⋯+ξ_τ$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0, ∞)$, we study the limits of the ratios of tails $\overline{F^{*\tau}}(x)/\overline{F}(x)$ as $x→∞$ (here, $τ$ is a counting random variable which does not depend on $\{ξ_n\}_{n≥1})$. We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.

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Denis Denisov. Serguei Foss. Dmitry Korshunov. "On lower limits and equivalences for distribution tails of randomly stopped sums." Bernoulli 14 (2) 391 - 404, May 2008. https://doi.org/10.3150/07-BEJ111

Information

Published: May 2008
First available in Project Euclid: 22 April 2008

zbMATH: 1157.60315
MathSciNet: MR2544093
Digital Object Identifier: 10.3150/07-BEJ111

Keywords: convolution equivalence , Convolution tail , lower limit , randomly stopped sums , subexponential distribution

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

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Vol.14 • No. 2 • May 2008
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