Discrete Mathematics & Theoretical Computer Science (Jan 2008)
On subcritical multi-type branching process in random environment
Abstract
We investigate a multi-type Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Suppose that the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices has negative mean and assuming some additional conditions, we find the asymptotics of the survival probability at time $n$ as $n \to \infty$.
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