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February, 1975 Application of Space-time Harmonic Functions to Branching Processes
Thomas H. Savits
Ann. Probab. 3(1): 61-69 (February, 1975). DOI: 10.1214/aop/1176996448

Abstract

In attempting to determine the growth properties of a branching process (b.p.), a standard method of attack is to look for the appropriate martingale. Here we show that for many b.p., this really corresponds to looking for the harmonic functions associated with the space-time process. As a particular application of the above we show that in the case of the classical Galton-Watson continuous time process with $m < \infty$ there exists constants $c(t)$ such that $Z_t/c(t)$ converges w.p. 1 to a nontrivial random variable.

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Thomas H. Savits. "Application of Space-time Harmonic Functions to Branching Processes." Ann. Probab. 3 (1) 61 - 69, February, 1975. https://doi.org/10.1214/aop/1176996448

Information

Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60079
MathSciNet: MR388565
Digital Object Identifier: 10.1214/aop/1176996448

Subjects:
Primary: 60J80
Secondary: 60G45

Keywords: a.s. convergence , branching process , martingale , space-time harmonic function

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 1 • February, 1975
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