Markov chains with stable drift and law of large numbers on hypergroups

On a large class of non compact one dimensional hypergroups we show that every random walk (X(n))(n greater than or equal to 0) with finite expectation, has a drift which tends to a limit D at infinity. By elementary results on Markov chains of independent interest, we can then deduce a law of large numbers which, in most cases, takes the classical form lim X(n)/n = D a.s.