Selfdecomposable Laws Associated with Hyperbolic Functins

TL;DR

This paper explores the connection between hyperbolic functions and selfdecomposable probability distributions, revealing their association with background driving Lévy processes and providing interpretations via Bessel processes and local times.

Contribution

It establishes a novel link between hyperbolic functions and selfdecomposable laws, including their background Lévy processes and interpretations through Bessel-related stochastic processes.

Findings

Hyperbolic functions are associated with selfdecomposable distributions.

Background Lévy processes are characterized via Bessel processes.

Distributions of Y(1) are interpreted through Bessel squared processes and local times.

Abstract

It is shown that the hyperbolic functions can be associated with selfdecomposable distributions (in short: SD probability distributions or L\'evy class L probability laws). Consequently, they admit associated background driving L\'evy processes $Y$ (BDLP Y). We interpret the distributions of Y(1) via Bessel squared processes, Bessel bridges and local times.