Electronic Communications in Probability

Transition density of a hyperbolic Bessel process

Andrzej Pyć and Tomasz Żak

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 50, 10 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J65: Brownian motion [See also 58J65]

hyperbolic Bessel process hyperbolic Brownian motion

Creative Commons Attribution 4.0 International License.


Pyć, Andrzej; Żak, Tomasz. Transition density of a hyperbolic Bessel process. Electron. Commun. Probab. 21 (2016), paper no. 50, 10 pp. doi:10.1214/16-ECP8. https://projecteuclid.org/euclid.ecp/1469557024

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