Open Access
2016 Transition density of a hyperbolic Bessel process
Andrzej Pyć, Tomasz Żak
Electron. Commun. Probab. 21: 1-10 (2016). DOI: 10.1214/16-ECP8


We investigate the transition density of a hyperbolic Bessel process for integer dimensions and show a link between transition densities of a hyperbolic Brownian motion and a Bessel process in the same dimension. Using the so-called Millson’s formula for the densities of hyperbolic Brownian motion we also show a link between transition density of $n$-dimensional hyperbolic Bessel process and $2$-dimensional (if $n$ is even) or $3$-dimensional (if $n$ is odd) hyperbolic Brownian motion. This helps us to get explicit formulas for the Bessel process transition density.


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Andrzej Pyć. Tomasz Żak. "Transition density of a hyperbolic Bessel process." Electron. Commun. Probab. 21 1 - 10, 2016.


Received: 13 February 2016; Accepted: 5 July 2016; Published: 2016
First available in Project Euclid: 26 July 2016

zbMATH: 1345.60092
MathSciNet: MR3533282
Digital Object Identifier: 10.1214/16-ECP8

Primary: 60J60
Secondary: 60J65

Keywords: hyperbolic Bessel process , hyperbolic Brownian motion

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