Electron. J. Probab. 27, paper no. 21 (2022) 1-17.
Ian Melbourne and Dalia Terhesiu
Abstract
We give a short analytic proof of large local 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.