Large deviations for stable like random walks on $\mathbb Z^d$ with applications to random walks on wreath products

Abstract

We derive Donsker-Vardhan type results for functionals of the occupation times when the underlying random walk on $\mathbb Z^d$ is in the domain of attraction of an operator stable law on $\mathbb R^d$. Applications to random walks on wreath products (also known as lamplighter groups) are given.