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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).

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains