## The Annals of Mathematical Statistics

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

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

#### 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