Sharp estimates on the tail behavior of a multistable distribution

TL;DR

This paper extends the understanding of tail behavior from symmetric alpha-stable distributions to multistable distributions, which generalize stable distributions by allowing the stability parameter to vary.

Contribution

It provides sharp estimates on the tail behavior of multistable distributions, a recent generalization of alpha-stable distributions with a variable stability parameter.

Findings

Tail of multistable distributions asymptotically behaves as a power function

Extension of classical stable distribution tail results to multistable case

Provides precise estimates for tail decay rates

Abstract

Multistable distributions, which have been introduced recently by Falconer, L\'evy V\'ehel and their co-authors, are natural generalizations of symmetric "alpha" stable distributions; roughly speaking, they are obtained by replacing the constant parameter "alpha" by a (Lebesgue) mesurable function. It is known that the tail of a symmetric "alpha" stable distribution asymptotically behaves as a power function with exponent "-alpha"; in this article we extend the latter result to the setting of multistable distributions.