On hyperbolic Bessel processes and beyond
Jacek Jakubowski , Maciej Wiśniewolski
AbstractWe 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.
|Journal series||Bernoulli, ISSN 1350-7265|
|Publication size in sheets||0.85|
|Score|| = 25.0, 31-12-2019, ArticleFromJournal|
= 30.0, 31-12-2019, ArticleFromJournal
|Publication indicators||= 5; : 2013 = 1.905; : 2013 = 1.296 (2) - 2013=1.392 (5)|
|Citation count*||8 (2016-03-11)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.