Sudden Extinction of a Critical Branching Process in Random Environment
نویسنده
چکیده
Abstract. Let T be the extinction moment of a critical branching process Z = (Zn, n ≥ 0) in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the process Z at moment n → ∞, and show that if the logarithm of the (random) expectation of the offspring number belongs to the domain of attraction of a non-gaussian stable law then the extinction occurs owing to very unfavorable environment forcing the process, having at moment T − 1 exponentially large population, to die out. We also give an interpretation of the obtained results in terms of random walks in random environment.
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