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Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 1, Pages 28–49 (Mi tvp3945)  

This article is cited in 1 scientific paper (total in 1 paper)

Weak Convergence of Random Sums

V. M. Kruglova, B. Zhangb

a 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.

DOI: https://doi.org/10.4213/tvp3945

Full text: PDF file (2247 kB)

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

Bibliographic databases:

Received: 02.02.2000

Citation: V. M. Kruglov, B. Zhang, “Weak Convergence of Random Sums”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 28–49; Theory Probab. Appl., 46:1 (2002), 39–57

Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 1
\pages 39--57
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    This publication is cited in the following articles:
    1. Korolev V.Yu. Zeifman A.I., “On convergence of the distributions of random sequences with independent random indexes to variance–mean mixtures”, Stoch. Models, 32:3 (2016), 414–432  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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