Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

Loïc Hervé; Françoise Pène

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arXiv · 1506.07659

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

Loïc Hervé·Françoise Pène

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Abstract

We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] 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).

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BibTeX RIS

Loïc Hervé, Françoise Pène. 2015-06-25. Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains. https://arxiv.org/abs/1506.07659

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