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

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.


pdf file , link to journal version