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, . Our method simultaneously covers lattice and nonlattice distributions (and mixtures thereof), bypassing aperiodicity considerations. The proof applies also to the dynamical setting.
DT was partially supported by EPSRC grant EP/S019286/1.
We are grateful to the referees for several helpful comments and suggestions.
"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