Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

Loïc Hervé (1) , Françoise Pene (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We study properties of the Laplace transforms of non-negative additive func-tionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [16] to study bifurcating processes with ancestral dependence. We develop a general approach based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including a linear autoregressive model. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Loïc Hervé, Françoise Pene. Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains. 2015. ⟨hal-01167914v3⟩