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PROBABILITÉ DE SURVIE D'UN PROCESSUS DE BRANCHEMENT DANS UN ENVIRONNEMENT ALÉATOIRE MARKOVIEN

Abstract : The purpose of this thesis is to study the survival probability of a branching process in markovian random environment and expand in this framework some known results which have been developed for a branching processus in i.i.d. random environment, the core of the study is based on the use of the local limit theorem for a centered random walk (Sn)n 0 on R with markovian increasements and for (mn)n 0, where mn = min (0; S1; ; Sn). In order to treat the case of a markovian random environment, we establish firstly a local limit theorem for a semi-markovian chain on R, which improves certain results developed initially by E. L. Presman (see [22] and [23]). We then use these results to study the asymptotic behavior of a critical branching process in markovian environment. The main results of this thesis are announced in Comptes Rendus de l'Académie des Sciences ([21]). A detailed paper is submitted for publication in the Journal of Theoretical Probability. In this thesis, we specify all the statements and the detailed proofs.
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Submitted on : Monday, July 4, 2011 - 11:33:49 AM
Last modification on : Thursday, March 5, 2020 - 5:32:36 PM
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Yinna Ye. PROBABILITÉ DE SURVIE D'UN PROCESSUS DE BRANCHEMENT DANS UN ENVIRONNEMENT ALÉATOIRE MARKOVIEN. Mathématiques [math]. Université François Rabelais - Tours, 2011. Français. ⟨tel-00605751⟩

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