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, 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.
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