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On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums
Kybernetika, Tome 55 (2019) no. 6, pp. 961-975 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2019-6-0961
Classification : 60E07, 60F05, 60F99, 60G50
Keywords: geometric random sums; Gnedenko's transfer theorem; Zolotarev probability metric 
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     title = {On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums},
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     year = {2019},
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Hung, Tran Loc; Kien, Phan Tri; Nhut, Nguyen Tan. On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums. Kybernetika, Tome 55 (2019) no. 6, pp. 961-975. doi: 10.14736/kyb-2019-6-0961

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