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January, 1987 Limiting Distributions and Regeneration Times for Multitype Branching Processes with Immigration in a Random Environment
Eric S. Key
Ann. Probab. 15(1): 344-353 (January, 1987). DOI: 10.1214/aop/1176992273

Abstract

Sufficient conditions for the existence of a limiting distribution for a multitype branching process with immigration in a random environment, $Z(t)$, are given. In the case when the environment is an independent, identically distributed sequence, sufficient conditions are given which insure that the tail of the distribution of $\nu = \inf\{t > 0: Z(t) = 0\}$ decreases exponentially fast, and an application of this fact to random walk in a random environment is indicated.

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Eric S. Key. "Limiting Distributions and Regeneration Times for Multitype Branching Processes with Immigration in a Random Environment." Ann. Probab. 15 (1) 344 - 353, January, 1987. https://doi.org/10.1214/aop/1176992273

Information

Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0623.60090
MathSciNet: MR877607
Digital Object Identifier: 10.1214/aop/1176992273

Subjects:
Primary: 60J10
Secondary: 60J15

Keywords: limiting distributions , Multitype branching process with immigration in a random environment , Products of random matrices , Random walk in a random environment , Regeneration times

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • January, 1987
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