Un principe d'invariance pour une classe de marches p-corrélées sur ℤd

Abstract

Let ζ be a Markov chain on a finite state spaceD,fa function fromDto ℝd, andSn= ∑k=1nf(ζk). We prove an invariance theorem forSand derive an explicit expression of the limit covariance matrix. We give its exact value forp-reinforced random walks on ℤ2withp= 1, 2, 3.