LIMIT THEOREMS FOR CRITICAL BRANCHING PROCESSES IN A FINITE STATE SPACE MARKOVIAN ENVIRONMENT
Résumé
Let (Zn) n≥0 be a critical branching process in a random environment defined by a Markov chain (Xn) n≥0 with values in a finite state space X. Let Sn = n k=1 ln f X k (1) be the Markov walk associated to (Xn) n≥0 , where fi is the offspring generating function when the environment is i ∈ X. Conditioned on the event {Zn > 0}, we show the non degeneracy of the limit law of the normalized number of particles Zn/e Sn and determine the limit of the law of Sn √ n jointly with Xn. Based on these results we establish a Yaglom-type theorem which specifies the limit of the joint law of log Zn and Xn given Zn > 0.
Origine | Fichiers produits par l'(les) auteur(s) |
---|