English

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

Probability 2015-09-11 v3

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).

Keywords

Cite

@article{arxiv.1506.07659,
  title  = {Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains},
  author = {Loïc Hervé and Françoise Pène},
  journal= {arXiv preprint arXiv:1506.07659},
  year   = {2015}
}