On hyperbolic Bessel processes and beyond

Jacek Jakubowski , Maciej Wiśniewolski


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.
Author Jacek Jakubowski (FMIS / DSPFM) - [University of Warsaw (UW)]
Jacek Jakubowski,,
- Department of Stochastic Processes and Financial Mathematics
- Uniwersytet Warszawski
, Maciej Wiśniewolski
Maciej Wiśniewolski,,
Journal seriesBernoulli, ISSN 1350-7265
Issue year2013
Publication size in sheets0.85
ASJC Classification2613 Statistics and Probability
URL https://projecteuclid.org/euclid.bj/1386078609#ui-tabs-1
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 25.0, 31-12-2019, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 31-12-2019, ArticleFromJournal
Publication indicators WoS Citations = 5; Scopus SNIP (Source Normalised Impact per Paper): 2013 = 1.905; WoS Impact Factor: 2013 = 1.296 (2) - 2013=1.392 (5)
Citation count*8 (2016-03-11)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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