A criterion of convergence of nonrandomly centered random sums of independent identically distributed random variables
type: Item
instance of: scholarly article
title: A criterion of convergence of nonrandomly centered random sums of independent identically distributed random variables
zbMATH Open document ID: 0913.60043
DOI: 10.1007/BF02362284
author: V. Yu. Korolev
author: V. M. Kruglov
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-11-24T00:00:00Z
review text: The authors present necessary and sufficient conditions for the weak convergence of non-randomly centered random sums of independent identically distributed random variables in the double array scheme under the assumption that in each sum the indices and the summands are independent. However, in the general case, necessary and sufficient conditions of weak convergence of non-randomly centered random sums of independent summands in the double scheme remained unknown until recently. We hope to discover such conditions with the help of the criterion of weak compactness of random sums which was published by the reviewer [Teor. Veroyatn. Primen 43, No. 2, 248-271 (1998)].
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1213220
zbMATH Keywords: weak convergence
zbMATH Keywords: weak compactness
MaRDI profile type: Publication
cites work: The asymptotic distribution of the sum of a random number of random variables
cites work: Q5637695
cites work: Limit Theorems for the Distributions of the Sums of a Random Number of Random Variables
cites work: Q4693044
cites work: Q3357188
cites work: Q4275980
cites work: Q4845571
cites work: A Necessary and Sufficient Condition for Convergence in Law of Random Sums of Random Variables Under Nonrandom Centering
cites work: Convergence in law of random sums with non-random centering
cites work: Convergence of nonrandomly centered random sums
cites work: Weak Compactness of Random Sumsof Independent Random Variables
cites work: Q4881149
cites work: Q4720452
cites work: Q5829358
full work available at URL: https://doi.org/10.1007/bf02362284
OpenAlex ID: W2010825548
description: scientific article; zbMATH DE number 1213220