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

Ian Melbourne; Dalia Terhesiu

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arXiv · 2009.02514

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

Ian Melbourne·Dalia Terhesiu

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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, $α\in(0,1)\cup(1,2]$. 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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Ian Melbourne, Dalia Terhesiu. 2022-02-14. Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems. https://arxiv.org/abs/2009.02514

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