Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems

Abstract

We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate α-stable law, $\mathit{\alpha }\in (0,1)\cup (1,2]$. Our method simultaneously covers lattice and nonlattice distributions (and mixtures thereof), bypassing aperiodicity considerations. The proof applies also to the dynamical setting.