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December, 1972 Limit Theorems for the Distributions of the Sums of a Random Number of Random Variables
D. Szasz
Ann. Math. Statist. 43(6): 1902-1913 (December, 1972). DOI: 10.1214/aoms/1177690861

Abstract

A necessary condition is given for the convergence of distributions of the sums of a random number of independent random variables. This is made on the basis of a theorem which gives sufficient conditions for the convergence of distributions of randomly stopped stochastic processes. The random indices are supposed to be independent of the sequence of summands.

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D. Szasz. "Limit Theorems for the Distributions of the Sums of a Random Number of Random Variables." Ann. Math. Statist. 43 (6) 1902 - 1913, December, 1972. https://doi.org/10.1214/aoms/1177690861

Information

Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0277.60015
MathSciNet: MR358942
Digital Object Identifier: 10.1214/aoms/1177690861

Rights: Copyright © 1972 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December, 1972
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