  We study the asymptotic behaviour of additive functionals of random walks in
random scenery. We establish bounds for the moments of the local time of the
Kesten and Spitzer process.These bounds combined with a previous moment
convergence result (and an ergodicity result) imply the convergence in
distribution of additive observables (with a normalization in n^(1/4)).When the
sum of the observable is null, the previous limit vanishes and we prove the
convergence in the sense of moments (with a normalization in n^(1/8)).

Dynamical Systems;Probability