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June, 1974 A Note on the Supercritical Branching Processes with Random Environments
Norman Kaplan
Ann. Probab. 2(3): 509-514 (June, 1974). DOI: 10.1214/aop/1176996668


Some further results in the theory of Galton Watson processes are extended to the more general set up of a branching process with random environments. The random distribution function of the limit random variable in the supercritical case (Athreya and Karlin, Ann. Math. Statist., 40 (1969) 743-763) is investigated, and a zero-one law is established. It is shown that this random distribution function is w.p. 1. either absolutely continuous on $(0, \infty)$ with only a jump at the origin or w.p. 1. it is singular. A set of conditions is given under which the former case holds.


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Norman Kaplan. "A Note on the Supercritical Branching Processes with Random Environments." Ann. Probab. 2 (3) 509 - 514, June, 1974.


Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0293.60079
MathSciNet: MR356265
Digital Object Identifier: 10.1214/aop/1176996668

Primary: 60J85
Secondary: 60J80

Keywords: branching process , branching process with random environment , random environment , stationary ergodic process , supercritical branching process

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • June, 1974
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