AN INVARIANCE-PRINCIPLE FOR A CLASS OF P-REINFORCED WALKS ON Z(D)

Let zeta be a Markov chain on a finite state space D, f a function fro m D to R-d, and S-n = Sigma(k=1)(n) f(zeta(k)). We prove an invariance theorem for S and derive an explicit expression of the limit covarian ce matrix. We give its exact value for p-reinforced random walks on Z( 2) with p = 1, 2, 3.