Integral Representations for the Hartman–Watson Density

Yuu Hariya

doi:10.1007/s10959-020-01067-0

Integral Representations for the Hartman–Watson Density

Yuu Hariya

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	209-230
Number of pages	22
Journal	Journal of Theoretical Probability
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s10959-020-01067-0
Publication status	Published - 2022 Mar
Externally published	Yes

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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10.1007/s10959-020-01067-0

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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{\textquoteright}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.",

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N2 - 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.

AB - 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.

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Integral Representations for the Hartman–Watson Density

Abstract

Keywords

ASJC Scopus subject areas

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