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

Electronic Journal of Probability, vol. 27

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∈(0,1)∪(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, United Kingdom

2. Dalia Terhesiu Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

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