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Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems
Published 5 Sep 2020 in math.PR and math.DS | (2009.02514v3)
Abstract: We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate $\alpha$-stable law, $\alpha\in(0,1)\cup(1,2]$. Our method simultaneously covers lattice and nonlattice distributions (and mixtures thereof), bypassing aperiodicity considerations. The proof applies also to the dynamical setting.
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