This article is cited in 6 papers

Weak Convergence of Random Sums

V. M. Kruglov^a, B. Zhang<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Peking University

Abstract: Weak convergence of nonrandomly centered sums of independent random variables with a random number of summands is investigated under the assumption that the number of summands and the summands themselves are independent and the summands are uniformly asymptotically negligible. The theorems proved in this paper are analogues of well-known limit theorems for sums of independent random variables with a nonrandom number of summands.

Keywords: weak convergence, weak compactness, convergence in probability, random sum, distribution function, characteristic function.

Received: 02.02.2000

DOI: 10.4213/tvp3945

 English version: Theory of Probability and its Applications, 2002, 46:1, 39–57

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