Generalized moments of sums with heavy-tailed random summands

Dirma, Mantas; Nakliuda, Neda; Šiaulys, Jonas

doi:10.1007/s10986-023-09606-y

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2024

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“…Proof of this part is similar to the proof of part (i) of Proposition 1. Namely, for λ > 0 and K ≥ 2 by using (10), we obtain that…”

Section: Proof Of Propositionmentioning

confidence: 99%

Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

Leipus,

Šiaulys,

Danilenko

et al. 2024

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This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided.

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“…Proof of this part is similar to the proof of part (i) of Proposition 1. Namely, for λ > 0 and K ≥ 2 by using (10), we obtain that…”

Section: Proof Of Propositionmentioning

confidence: 99%