On weak generalized stability and (c,d)-pseudostable random variables via functional equations

TL;DR

This paper explores the concept of weak generalized stability in distributions, focusing on symmetric weakly stable distributions and their characterization through functional equations, extending classical stability concepts.

Contribution

It introduces the notion of stability with respect to weak generalized convolution and characterizes symmetric weakly stable distributions via functional equations.

Findings

Characterization of symmetric weakly stable distributions

Extension of classical stability concepts to weak generalized convolution

Solution of functional equations for distribution characterization

Abstract

In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical convolution, characterization of distributions stable in the sense of the weak generalized convolution depends on solving some functional equations in the class of characteristic functions.