Integral Representations for the Hartman–Watson Density

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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.

Original languageEnglish
Pages (from-to)209-230
Number of pages22
JournalJournal of Theoretical Probability
Volume35
Issue number1
DOIs
Publication statusPublished - 2022 Mar
Externally publishedYes

Keywords

  • Brownian motion
  • Exponential functional
  • Hartman–Watson law

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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