Departement de Mathematiques, Université de Tours, Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France
Abstract:
Let be a homogeneous Markov chain on an unbounded Borel subset of with a drift function which tends to a limit at infinity. Under a very simple hypothesis on the chain we prove that converges in distribution to a normal law where the variance depends on the asymptotic behaviour of . When goes to zero quickly enough and , the random centering may be replaced by These results are applied to the case of random walks on some hypergroups.