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Article Dans Une Revue Stochastic Processes and their Applications Année : 2019

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

Ion Grama
Ronan Lauvergnat

Résumé

Let (Z n) n 0 be a branching process in a random environment defined by a Markov chain (X n) n 0 with values in a finite state space X. Let P i be the probability generated by the trajectories of (X n) n 0 starting at X 0 = i ∈ X. We study the asymptotic behaviour of the joint survival probability P i (Z n > 0 , X n = j), j ∈ X as n → +∞ in the critical and strongly, intermediate and weakly subcritical cases.
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Dates et versions

hal-02019644 , version 1 (23-06-2020)

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Ion Grama, Ronan Lauvergnat, Emile Le Page. The survival probability of critical and subcritical branching processes in finite state space markovian environment. Stochastic Processes and their Applications, 2019, 129, pp.2485-2527. ⟨10.1016/j.spa.2018.07.016⟩. ⟨hal-02019644⟩
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