The random integral representation hypothesis revisited : new classes of s-selfdecomposable laws

TL;DR

This paper introduces new subclasses of s-selfdecomposable probability measures, characterized through random integrals and their relations to classical selfdecomposable distributions, expanding the theoretical understanding of these classes.

Contribution

It defines and analyzes new subclasses of s-selfdecomposable laws using random integral representations and explores their connections with classical selfdecomposable distributions.

Findings

New subclasses al^{<\u03b1>}\u00a0are characterized by their characteristic functions.

Relations between these subclasses and the classical Le9vy class L are established.

Descriptions involve random integrals, spectral measures, and characteristic functions.

Abstract

For $\,0<\alpha\le \infty$, new subclasses $\,\mathcal{U}^{<\alpha>}$ of the class $\,\mathcal{U}$, of s-selfdecomposable probability measures, are studied. They are described by random integrals, by their characteristic functions and their L\'evy spectral measures. Also their relations with the classical L\'evy class $L$ of selfdecomposable distributions are investigated.