Mixing properties for Markovian dynamical systems.

Summary This thesis deals with the mixing properties of Markovian dynamical systems. The study of the associated transfer operator leads to estimates of the decay of correlations or mixing speed. These estimates allow to establish probabilistic theorems, for example the central limit theorem, for systems which do not possess, in general, the spectral hole property. The first part deals with Markov dynamics on a finite state space, associated with a non-Holderian potential. The decay of correlations depends on the continuity modulus of this potential. Moreover, these systems are stochastically stable. In a second part, we are interested in Markovian systems on a countable infinite state space. The decay of the correlations depends on the contribution to the transfer operator of the complementary of a finite number of cylinders. Effective estimates are given for non-uniformly dilating applications and for birth and death processes.