Lower deviations of branching processes in random environment with geometrical offspring distributions

Makoto Nakashima

Stochastic Processes and their Applications, 2013, vol. 123, issue 9, 3560-3587

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 Zn the population at the n-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 {0Keywords: Branching processes; Random environment; Large deviations (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2013.04.013

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