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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 1, Pages 28–49
DOI: https://doi.org/10.4213/tvp3945 (Mi tvp3945) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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
Full-text PDF (2247 kB) Citations (6)
DOI: https://doi.org/10.4213/tvp3945
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
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 1, Pages 39–57
DOI: https://doi.org/10.1137/S0040585X97978713
Bibliographic databases:
Document Type: Article
Language: Russian
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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\paper Weak Convergence of Random Sums
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\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 1
\pages 39--57
\crossref{https://doi.org/10.1137/S0040585X97978713}
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  • https://doi.org/10.4213/tvp3945
  • https://www.mathnet.ru/eng/tvp/v46/i1/p28
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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