Integral representations for the Hartman--Watson density

Yuu Hariya

Published 2019-04-01Version 1

This paper concerns the density of the Hartman--Watson law. Yor (1980) obtained an integral formula that gives a closed-form expression of the Hartman--Watson density. In this paper, based on Yor's formula, we provide alternative integral representations for the density. As an immediate application, we recover in part a Dufresne's result (2001) that exhibits remarkably simple representations for densities of the laws of exponential additive functionals of Brownian motion.