Open Access
February, 1977 Limit Theorems for Branching Processes in a Random Environment
David Tanny
Ann. Probab. 5(1): 100-116 (February, 1977). DOI: 10.1214/aop/1176995894


In this paper, growth of branching processes in random environment is considered. In particular it is shown that this process either "explodes" at an exponential rate or else becomes extinct w.p.1. A classification theorem outlining the cases of "explosion or extinction" is given. To prove these theorems, the associated branching process (the process conditioned on each particle having infinite descent) and the reduced branching process (the particles of the process having infinite descent) are introduced. The method of proof used, in general, is direct probabilistic computation, in contrast with the classical functional iteration method.


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David Tanny. "Limit Theorems for Branching Processes in a Random Environment." Ann. Probab. 5 (1) 100 - 116, February, 1977.


Published: February, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0368.60094
MathSciNet: MR426189
Digital Object Identifier: 10.1214/aop/1176995894

Primary: 60J80
Secondary: 60F15

Keywords: associated branching process in a random environment , Branching processes in random environments , reduced branching process in a random environment

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • February, 1977
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