Electronic Communications in Probability

Transition density of a hyperbolic Bessel process

Andrzej Pyć and Tomasz Żak

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1469557024

Digital Object Identifier
doi:10.1214/16-ECP8

Mathematical Reviews number (MathSciNet)
MR3533282

Zentralblatt MATH identifier
1345.60092

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

Keywords
hyperbolic Bessel process hyperbolic Brownian motion

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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