Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

摘要

We study properties of the Laplace transforms of non-negative additivefunctionals of Markov chains. We are namely interested in a multiplicativeergodicity property used in [18] to study bifurcating processes with ancestraldependence. We develop a general approach based on the use of the operatorperturbation method. We apply our general results to two examples of Markovchains, including a linear autoregressive model. In these two examples theoperator-type assumptions reduce to some expected finite moment conditions onthe functional (no exponential moment conditions are assumed in this work).