Multitype subcritical branching processes in a random environment

Abstract

We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable XeX has zero mean, we find the asymptotics of the survival probability at time n as n → ∞.