The Annals of Mathematical Statistics

Limit Distributions of a Branching Stochastic Process

Howard H. Stratton, Jr. and Howard G. Tucker

Full-text: Open access

Abstract

A population of particles is considered whose size $X_N(t)$ changes according to a branching stochastic process. The purpose of this paper is to find an approximate distribution of $X_N(t)$ when $t$ is fixed (not necessarily large) but the initial size of the population, $N$, is large. If $N$ is allowed to tend to infinity, and if the parameters of the process are made to change in a way analogous to the Poisson approximation of a binomial distribution, then it is shown that a limiting distribution of the process $X_N(t) - N$ exists as $N \rightarrow \infty$, and this limiting distribution is the distribution of a continuous process with independent increments. The relation between the parameters of the infinitely divisible distribution of the limiting process and the sequence of branching processes is exhibited.

Article information

Source
Ann. Math. Statist., Volume 35, Number 2 (1964), 557-565.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703555

Digital Object Identifier
doi:10.1214/aoms/1177703555

Mathematical Reviews number (MathSciNet)
MR160272

Zentralblatt MATH identifier
0245.60064

JSTOR
links.jstor.org

Citation

Stratton, Howard H.; Tucker, Howard G. Limit Distributions of a Branching Stochastic Process. Ann. Math. Statist. 35 (1964), no. 2, 557--565. doi:10.1214/aoms/1177703555. https://projecteuclid.org/euclid.aoms/1177703555


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