Open Access
Translator Disclaimer
2022 Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems
Ian Melbourne, Dalia Terhesiu
Author Affiliations +
Electron. J. Probab. 27: 1-17 (2022). DOI: 10.1214/22-EJP750

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.

Funding Statement

DT was partially supported by EPSRC grant EP/S019286/1.

Acknowledgments

We are grateful to the referees for several helpful comments and suggestions.

Citation

Download Citation

Ian Melbourne. Dalia Terhesiu. "Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems." Electron. J. Probab. 27 1 - 17, 2022. https://doi.org/10.1214/22-EJP750

Information

Received: 11 September 2020; Accepted: 30 January 2022; Published: 2022
First available in Project Euclid: 11 February 2022

Digital Object Identifier: 10.1214/22-EJP750

Subjects:
Primary: 37A50 , 37D20 , 60F10

Keywords: local large deviations , multivariate stable laws

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.27 • 2022
Back to Top