Sharp bounds for the tails of functionals of Markov chains

This paper is devoted to establishing sharp bounds for deviation probabilities of partial sums Σⁿ_i=1 f(X _i), where X = (X_n)_n∈N is a positive recurrent Markov chain and f is a real valued function defined on its state space. Combining the regenerative method to the Esscher transformation, these estimates are shown in particular to generalize probability inequalities proved in the independent i.i.d. case to the Markovian setting for (not necessarily uniformly) geometrically ergodic chains.