On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums

Tran Loc Hung; Phan Tri Kien; Nguyen Tan Nhut

Kybernetika (2019)

  • Volume: 55, Issue: 6, page 961-975
  • ISSN: 0023-5954

Abstract

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Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated.

How to cite

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Hung, Tran Loc, Kien, Phan Tri, and Nhut, Nguyen Tan. "On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums." Kybernetika 55.6 (2019): 961-975. <http://eudml.org/doc/297113>.

@article{Hung2019,
abstract = {Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated.},
author = {Hung, Tran Loc, Kien, Phan Tri, Nhut, Nguyen Tan},
journal = {Kybernetika},
keywords = {geometric random sums; Gnedenko's transfer theorem; Zolotarev probability metric},
language = {eng},
number = {6},
pages = {961-975},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums},
url = {http://eudml.org/doc/297113},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Hung, Tran Loc
AU - Kien, Phan Tri
AU - Nhut, Nguyen Tan
TI - On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 6
SP - 961
EP - 975
AB - Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated.
LA - eng
KW - geometric random sums; Gnedenko's transfer theorem; Zolotarev probability metric
UR - http://eudml.org/doc/297113
ER -

References

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