The Annals of Mathematical Statistics

Limit Theorems for the Distributions of the Sums of a Random Number of Random Variables

D. Szasz

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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.

Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 1902-1913.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177690861

Digital Object Identifier
doi:10.1214/aoms/1177690861

Mathematical Reviews number (MathSciNet)
MR358942

Zentralblatt MATH identifier
0277.60015

JSTOR
links.jstor.org

Citation

Szasz, D. Limit Theorems for the Distributions of the Sums of a Random Number of Random Variables. Ann. Math. Statist. 43 (1972), no. 6, 1902--1913. doi:10.1214/aoms/1177690861. https://projecteuclid.org/euclid.aoms/1177690861


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