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Transition density of a hyperbolic Bessel process. (English) Zbl 1345.60092

Summary: 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 the transition density of an \(n\)-dimensional hyperbolic Bessel process and a \(2\)-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.

MSC:

60J60 Diffusion processes
60J65 Brownian motion
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