On monotone convolution and monotone infinite divisivility

TL;DR

This paper investigates properties of monotone convolutions, establishing criteria for infinite divisibility and analyzing the time evolution of convolution semigroups, with parallels to classical Lévy process results.

Contribution

It provides new criteria for infinite divisibility in monotone convolutions and clarifies the analogy with classical Lévy process properties.

Findings

Criteria for infinite divisibility established

Characterizations of subordinators and stable distributions

Time evolution of convolution semigroups analyzed

Abstract

This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of L\'{e}vy processes hold such as characterizations of subordinators and strictly stable distributions.