Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains
Résumé
This article is motivated by the quantitative study of the exponential growth of Markov-driven bifurcating processes [see Hervé et al., ESAIM: PS 23 (2019) 584–606]. In this respect, a key property is the multiplicative ergodicity, which deals with the asymptotic behaviour of some Laplace-type transform of nonnegative additive functional of a Markov chain. We establish a spectral version of this multiplicative ergodicity property in a general framework. Our approach is based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including linear autoregressive models. 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).
Mots clés
2010 Mathematics Subject Classification. Primary: 60J05 60J85 Markov processes quasicompacity operator perturbation ergodicity Laplace transform branching process age-dependent process Malthusian parameter
2010 Mathematics Subject Classification. Primary: 60J05
60J85 Markov processes
quasicompacity
operator
perturbation
ergodicity
Laplace transform
branching process
age-dependent process
Malthusian parameter
Domaines
Probabilités [math.PR]| Origine | Fichiers produits par l'(les) auteur(s) |
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