Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2437-2454.

On hyperbolic Bessel processes and beyond

Jacek Jakubowski and Maciej Wiśniewolski

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Abstract

We investigate distributions of hyperbolic Bessel processes. We find links between the hyperbolic cosine of hyperbolic Bessel processes and functionals of geometric Brownian motion. We present an explicit formula for the Laplace transform of the hyperbolic cosine of a hyperbolic Bessel process and some other interesting probabilistic representations of this Laplace transform. We express the one-dimensional distribution of a hyperbolic Bessel process in terms of other, known and independent processes. We present some applications including a new proof of Bougerol’s identity and its generalization. We characterize the distribution of the process which is the hyperbolic sine of hyperbolic Bessel process.

Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2437-2454.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078609

Digital Object Identifier
doi:10.3150/12-BEJ458

Mathematical Reviews number (MathSciNet)
MR3160560

Zentralblatt MATH identifier
1284.60150

Keywords
Bessel process Brownian motion hyperbolic Bessel process Laplace transform

Citation

Jakubowski, Jacek; Wiśniewolski, Maciej. On hyperbolic Bessel processes and beyond. Bernoulli 19 (2013), no. 5B, 2437--2454. doi:10.3150/12-BEJ458. https://projecteuclid.org/euclid.bj/1386078609


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