Integral Representations for the Hartman–Watson Density

Yuu Hariya ()
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Yuu Hariya: Tohoku University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 209-230

Abstract: Abstract This paper concerns the density of the Hartman–Watson law. Yor (Z Wahrsch Verw Gebiete 53:71–95, 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 result of Dufresne (Adv Appl Probab 33:223–241, 2001) that exhibits remarkably simple representations for the laws of exponential additive functionals of Brownian motion.

Keywords: Brownian motion; Exponential functional; Hartman–Watson law; Primary 60J65; Secondary 60J55; 60E10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01067-0

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