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June, 1964 Limit Distributions of a Branching Stochastic Process
Howard H. Stratton Jr., Howard G. Tucker
Ann. Math. Statist. 35(2): 557-565 (June, 1964). DOI: 10.1214/aoms/1177703555


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.


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Howard H. Stratton Jr.. Howard G. Tucker. "Limit Distributions of a Branching Stochastic Process." Ann. Math. Statist. 35 (2) 557 - 565, June, 1964.


Published: June, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0245.60064
MathSciNet: MR160272
Digital Object Identifier: 10.1214/aoms/1177703555

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 2 • June, 1964
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