Comptes Rendus
no. 5-6
Probability Theory
The survival probability of a critical branching process in a Markovian random environment

Presented by: Jean-Pierre Kahane

Emile Le Page1; Yinna Ye1, 2
1 LMAM, université de Bretagne-Sud, campus de Tohannic, BP 573, 56017 Vannes, France
2 LMPT, UFR sciences et techniques, université François-Rabelais, parc de Grandmont, 37200 Tours, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 301-304.

In this Note, we first prove a local limit theorem for a semi-Markov chain and then apply it to study the asymptotic behavior of the survival probability of a critical branching process in Markovian random environment.

Dans cette Note, nous montrons d'abord un théorème de la limite locale pour une chaîne semi-Markovienne. Nous appliquons ensuite ce résultat pour étudier le comportement asymptotique de la probabilité de survie d'un processus de branchement critique dans un milieu aléatoire Markovien.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.01.014

Emile Le Page 1; Yinna Ye 1, 2

1 LMAM, université de Bretagne-Sud, campus de Tohannic, BP 573, 56017 Vannes, France
2 LMPT, UFR sciences et techniques, université François-Rabelais, parc de Grandmont, 37200 Tours, France 
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Emile Le Page; Yinna Ye. The survival probability of a critical branching process in a Markovian random environment. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 301-304. doi : 10.1016/j.crma.2010.01.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.014/

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