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September 2018 The survival probability of a critical multi-type branching process in i.i.d. random environment
E. Le Page, M. Peigné, C. Pham
Ann. Probab. 46(5): 2946-2972 (September 2018). DOI: 10.1214/17-AOP1243

Abstract

We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type Galton–Watson process in i.i.d. random environments by using limit theorems for products of positive random matrices. Under suitable assumptions, the survival probability is proportional to $1/\sqrt{n}$.

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E. Le Page. M. Peigné. C. Pham. "The survival probability of a critical multi-type branching process in i.i.d. random environment." Ann. Probab. 46 (5) 2946 - 2972, September 2018. https://doi.org/10.1214/17-AOP1243

Information

Received: 1 October 2016; Revised: 1 November 2017; Published: September 2018
First available in Project Euclid: 24 August 2018

zbMATH: 06964352
MathSciNet: MR3846842
Digital Object Identifier: 10.1214/17-AOP1243

Subjects:
Primary: 60J80
Secondary: 60F17, 60K37

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 5 • September 2018
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