A central limit theorem for some one dimensional Markov chains and applications

Let (X(n)) be a homogenous Markov chain on a non bounded Borel subset of R with a drift which tends to a limit m(1) at infinity. Under very simple hypothesis, we give a CLT for (X(n)) which in some cases reduces to the classical form: n(-1/2)(X(n) - nm(1)) (c)--> N(0; sigma(2)). We apply these results to random walks on a class of one dimensional hypergroups.