2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165468Let $S=(S_k)_{k\geq 0}$ be a random walk on $\mathbb{Z}$ and $ξ=(ξ_{i})_{i\in\mathbb{Z}}$ a stationary random sequence of centered random variables, independent of $S$. We consider a random walk in random scenery that is the sequence of random variables $(Σ_n)_{n\geq 0}$ where $$Σ_n=\sum_{k=0}^n ξ_{S_k}, n\in\mathbb{N}.$$ Under a weak dependence assumption on the scenery $ξ$ we prove a functional limit theorem generalizing Kesten and Spitzer's theorem (1979).Probabilitytext