Boolean convolutions and regular variation

Article Type

Research Article

Publication Title

Alea

Abstract

In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the notion of classical and free subexponentiality. We show that the distributions with regularly varying tails belong to the class of Boolean subexponential distributions. As an application we also study the behaviour of the Belinschi-Nica map. Breiman's theorem studies the classical product convolution between regularly varying measures. We derive an analogous result to Breiman's theorem in case of multiplicative Boolean convolution. In proving these results we exploit the relationship of regular variation with different transforms and their Taylor series expansion.

First Page

961

Last Page

991

DOI

10.30757/ALEA.v15-36

Publication Date

1-1-2018

Comments

All Open Access, Bronze, Green

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