The Bessel function ratios $(b/a)^\nu K_\nu(as^{\frac{1}{2}}) (a > b > 0, \nu \in R)$ and $(b/a)^\nu I_\nu(as^{\frac{1}{2}})/I_\nu(bs^{\frac{1}{2}}) (0 < a < b, \nu > -1)$ are infinitely divisible Laplace transforms in $s > 0$. These results are derived as hitting times of the Bessel diffusion process. The infinite divisibility of the $t$-distribution is deduced as a limiting result. A relationship with the von Mises-Fisher distribution is also demonstrated.
Publié le : 1978-10-14
Classification:
Infinite divisibility,
$t$-distribution,
Laplace transform,
Bessel functions,
diffusion,
semigroup,
von Mises-Fisher distribution,
60J70,
33A40
@article{1176995427,
author = {Kent, John},
title = {Some Probabilistic Properties of Bessel Functions},
journal = {Ann. Probab.},
volume = {6},
number = {6},
year = {1978},
pages = { 760-770},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995427}
}
Kent, John. Some Probabilistic Properties of Bessel Functions. Ann. Probab., Tome 6 (1978) no. 6, pp. 760-770. http://gdmltest.u-ga.fr/item/1176995427/