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June, 1974 Some Results about Multidimensional Branching Processes with Random Environments
Norman Kaplan
Ann. Probab. 2(3): 441-455 (June, 1974). DOI: 10.1214/aop/1176996659


A multidimensional branching process with random environments is considered. Two results are proven about this process. The first proves that all nonzero states of the process are transient. Since the process in question is not Markov, the proof of this result is more involved than in the classical case. Our second result deals with the extinction of the process when we are in the critical case. We prove as in the classical theory that extinction occurs $\operatorname{w.p.}$1.


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Norman Kaplan. "Some Results about Multidimensional Branching Processes with Random Environments." Ann. Probab. 2 (3) 441 - 455, June, 1974.


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

zbMATH: 0293.60078
MathSciNet: MR378127
Digital Object Identifier: 10.1214/aop/1176996659

Primary: 60J85
Secondary: 60J80

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

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • June, 1974
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