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

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.