Article ID Journal Published Year Pages File Type
1155522 Stochastic Processes and their Applications 2013 28 Pages PDF
Abstract

We consider the branching processes in random environment. In this paper, we deal with the case of environments which are chosen stationary and ergodic from the finite set of geometrical offspring distributions. We denote by ZnZn the population at the nn-th generation. We show that the large deviation principle holds with a certain rate function for the total population when the environment satisfies some conditions. Also, we will show that the trajectory t→logZntn,t∈[0,1] converges to a deterministic function uniformly in probability conditioned on {0

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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