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

arXiv (Cornell University)

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, $α\in(0,1)\cup(1,2]$. Our method simultaneously covers lattice and nonlattice distributions (and mixtures thereof), bypassing aperiodicity considerations. The proof applies also to the dynamical setting.

Authors 2

1. Ian Melbourne

   University of Warwick

   Affiliation as printed

   Mathematics Institute , University of Warwick , Coventry , CV4 7AL , UK

2. Dalia Terhesiu Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut , University of Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands