Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains with application to age-dependent branching process

Loïc Hervé (1) , Sana Louhichi (2) , Françoise Pène (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IPS - Inférence Processus Stochastiques
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We study the exponential growth of bifurcating processes with ancestral dependence. We suppose here that the lifetimes of the cells are dependent random variables, that the numbers of new cells are random and dependent. Lifetimes and new cells's numbers are also assumed to be dependent. We illustrate our results by examples, including some Markov models. Our approach is related to the behaviour of the Laplace transform of nonnegative additive functional of Markov chains and require weak moment assumption (no exponential moment is needed).

Mots clés: operator; perturbation; ergodicity; Laplace transform; branching process; age-dependent process; Malthusian parameter; quasicompacity; Markov processes

Domaines: Probabilités [math.PR]

Loïc Hervé, Sana Louhichi, Françoise Pène. Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains with application to age-dependent branching process. 2017. ⟨hal-01425323⟩