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 $1/\sqrt{n}$.
Citation
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
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