Remarks on the density of the law of the occupation time for Bessel bridges and stable excursions

TL;DR

This paper investigates the smoothness and asymptotic properties of the densities related to occupation times of Bessel bridges and stable excursions, emphasizing the role of Riemann--Liouville fractional integrals.

Contribution

It provides new insights into the density behaviors of occupation times for Bessel bridges and stable excursions using fractional integral techniques.

Findings

Analyzed smoothness of occupation time densities

Derived asymptotic behaviors of these densities

Highlighted the importance of fractional integrals in the analysis

Abstract

Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these properties for functions defined by Riemann--Liouville fractional integrals.