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.
Laurent Saloff-Coste. Tianyi Zheng. "Large deviations for stable like random walks on $\mathbb Z^d$ with applications to random walks on wreath products." Electron. J. Probab. 18 1 - 35, 2013. https://doi.org/10.1214/EJP.v18-2439