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

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.

Citation

Download Citation

Andrzej Pyć. Tomasz Żak. "Transition density of a hyperbolic Bessel process." Electron. Commun. Probab. 21 1 - 10, 2016. https://doi.org/10.1214/16-ECP8

Information

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

Subjects:
Primary: 60J60
Secondary: 60J65

JOURNAL ARTICLE
10 PAGES


SHARE
Back to Top