SOME RESULTS ON ASYMPTOTIC BEHAVIORS OF RANDOM SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES

- Journal title : Communications of the Korean Mathematical Society
- Volume 25, Issue 1, 2010, pp.119-128
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2010.25.1.119

Title & Authors

SOME RESULTS ON ASYMPTOTIC BEHAVIORS OF RANDOM SUMS OF INDEPENDENT IDENTICALLY DISTRIBUTED RANDOM VARIABLES

Hung, Tran Loc; Thanh, Tran Thien;

Hung, Tran Loc; Thanh, Tran Thien;

Abstract

Let be a sequence of independent identically distributed (i.i.d.) random variables (r.vs.), defined on a probability space (,A,P), and let be a sequence of positive integer-valued r.vs., defined on the same probability space (,A,P). Furthermore, we assume that the r.vs. , are independent of all r.vs. , . In present paper we are interested in asymptotic behaviors of the random sum , , where the r.vs. , obey some defined probability laws. Since the appearance of the Robbins's results in 1948 ([8]), the random sums have been investigated in the theory probability and stochastic processes for quite some time (see [1], [4], [2], [3], [5]). Recently, the random sum approach is used in some applied problems of stochastic processes, stochastic modeling, random walk, queue theory, theory of network or theory of estimation (see [10], [12]). The main aim of this paper is to establish some results related to the asymptotic behaviors of the random sum , in cases when the , are assumed to follow concrete probability laws as Poisson, Bernoulli, binomial or geometry.

Keywords

random sum;independent identically distributed random variables;asymptotic behavior;Poisson law;Bernoulli law;binomial law;geometric law;

Language

English

Cited by

1.

2.

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