Integral representations for the Hartman--Watson density
arXiv:1904.00595 · doi:10.1007/s10959-020-01067-0
Abstract
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 the laws of exponential additive functionals of Brownian motion.
21 pages; this is an abridged version of the previous one, accepted for publication in the Journal of Theoretical Probability, with shortened Section 4