Moderate deviation principle for ergodic Markov chain. Lipschitz summands

For 1/2 < alpha < 1, we propose the MDP analysis for family [GRAPHICS] where (X-n)(n >= 0) be a homogeneous ergodic Markov chain, X-n is an element of R-d, when the spectrum of operator P. is continuous. The vector-valued function H is not assumed to be bounded but the Lipschitz continuity of H is required. The main helpful tools in our approach are Poisson's equation and Stochastic Exponential; the first enables to replace the original family by with a martingale M-n while the second to avoid the direct Laplace transform analysis.