TY - JOUR
T1 - Integral Representations for the Hartman–Watson Density
AU - Hariya, Yuu
N1 - Funding Information:
Supported in part by JSPS KAKENHI Grant Number 17K05288.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
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.
KW - Brownian motion
KW - Exponential functional
KW - Hartman–Watson law
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U2 - 10.1007/s10959-020-01067-0
DO - 10.1007/s10959-020-01067-0
M3 - Article
AN - SCOPUS:85099086481
SN - 0894-9840
VL - 35
SP - 209
EP - 230
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 1
ER -