On hyperbolic Bessel processes and beyond

Details On hyperbolic Bessel processes and beyond On hyperbolic Bessel processes and beyond

2011-06-27

arxiv.org/abs/1106.5485v1

Mathematics

Probability

Scientific paper

We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosinus of the hyperbolic Bessel processes and the functionals of geometric Brownian motion. We present an explicit formula of Laplace transform of hyperbolic cosinus of hyperbolic Bessel processes and some interesting different probabilistic representations of this Laplace transform. We express the one-dimensional distribution of hyperbolic Bessel process in terms of other, known and independent processes. We present some applications including a new proof of Bougerol's identity and it's generalization. We characterize the distribution of the process being hyperbolic sinus of hyperbolic Bessel processes.

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