The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Ion Grama, Ronan Lauvergnat and Émile Le Page

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2485-2527

Abstract: Let (Zn)n≥0 be a branching process in a random environment defined by a Markov chain (Xn)n≥0 with values in a finite state space X. Let Pi be the probability law generated by the trajectories of Xnn≥0 starting at X0=i∈X. We study the asymptotic behaviour of the joint survival probability PiZn>0,Xn=j, j∈X as n→+∞ in the critical and strongly, intermediate and weakly subcritical cases.

Keywords: Critical and subcritical branching process; Random environment; Markov chain; Survival probability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.07.016

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