Abstract
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.
Citation
John Kent. "Some Probabilistic Properties of Bessel Functions." Ann. Probab. 6 (5) 760 - 770, October, 1978. https://doi.org/10.1214/aop/1176995427
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