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October, 1978 Some Probabilistic Properties of Bessel Functions
John Kent
Ann. Probab. 6(5): 760-770 (October, 1978). DOI: 10.1214/aop/1176995427

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

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

Information

Published: October, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0402.60080
MathSciNet: MR501378
Digital Object Identifier: 10.1214/aop/1176995427

Subjects:
Primary: 60J70
Secondary: 33A40

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • October, 1978
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