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Randomly Stopped Sums with Generalized Subexponential Distribution
Version 1
: Received: 25 May 2023 / Approved: 26 May 2023 / Online: 26 May 2023 (07:33:51 CEST)
A peer-reviewed article of this Preprint also exists.
Karasevičienė, J.; Šiaulys, J. Randomly Stopped Sums with Generalized Subexponential Distribution. Axioms 2023, 12, 641. Karasevičienė, J.; Šiaulys, J. Randomly Stopped Sums with Generalized Subexponential Distribution. Axioms 2023, 12, 641.
Abstract
Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.
Keywords
subexponentiality; generalized subexponentiality; heavy tail; randomly stopped sum
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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