Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic indep...

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Autores principales:	Jonas Sprindys, Jonas Šiaulys
Formato:	article
Lenguaje:	EN
Publicado:	Vilnius University Press 2021
Materias:	sum of random variables asymptotic independence tail moment truncated moment heavy tail consistently varying distribution Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/65c62853d32c419884bd494bca83ca7c
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spelling	oai:doaj.org-article:65c62853d32c419884bd494bca83ca7c2021-12-02T17:47:37ZAsymptotic formulas for the left truncated moments of sums with consistently varying distributed increments10.15388/namc.2021.26.246081392-51132335-8963https://doaj.org/article/65c62853d32c419884bd494bca83ca7c2021-11-01T00:00:00Zhttps://www.journals.vu.lt/nonlinear-analysis/article/view/24608https://doaj.org/toc/1392-5113https://doaj.org/toc/2335-8963 In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks. Jonas SprindysJonas ŠiaulysVilnius University Pressarticlesum of random variablesasymptotic independencetail momenttruncated momentheavy tailconsistently varying distributionAnalysisQA299.6-433ENNonlinear Analysis, Vol 26, Iss 6 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	sum of random variables asymptotic independence tail moment truncated moment heavy tail consistently varying distribution Analysis QA299.6-433
spellingShingle	sum of random variables asymptotic independence tail moment truncated moment heavy tail consistently varying distribution Analysis QA299.6-433 Jonas Sprindys Jonas Šiaulys Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
description	In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.
format	article
author	Jonas Sprindys Jonas Šiaulys
author_facet	Jonas Sprindys Jonas Šiaulys
author_sort	Jonas Sprindys
title	Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
title_short	Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
title_full	Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
title_fullStr	Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
title_full_unstemmed	Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
title_sort	asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
publisher	Vilnius University Press
publishDate	2021
url	https://doaj.org/article/65c62853d32c419884bd494bca83ca7c
work_keys_str_mv	AT jonassprindys asymptoticformulasforthelefttruncatedmomentsofsumswithconsistentlyvaryingdistributedincrements AT jonassiaulys asymptoticformulasforthelefttruncatedmomentsofsumswithconsistentlyvaryingdistributedincrements
_version_	1718379471080259584

Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

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