A central limit theorem for Markov chains and applications to hypergroups

Let (X-n) be a homogeneous Markov chain on an unbounded Borel subset of R with a drift function d which tends to a limit m(1) at infinity. Under a very simple hypothesis on the chain we prove that n(-1/2) [GRAPHICS] converges in distribution to a normal law N(0, sigma(2)) where the variance sigma(2) depends on the asymptotic behaviour of (X-n). When d - m(1) goes to zero quickly enough and m(1) not equal 0, the random centering may be replaced by nm(1). These results are applied to the case of random walks on some hypergroups.