Geodesic
Hyperbolic Ornstein–Uhlenbeck process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 45-55 
A. N. Borodin. Hyperbolic Ornstein–Uhlenbeck process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 45-55. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a4/
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     author = {A. N. Borodin},
     title = {Hyperbolic {Ornstein{\textendash}Uhlenbeck} process},
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     year = {2015},
     volume = {441},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The the paper we continue the investigation of the class of hypergeometric diffusions started in [1]. The wide subclass of these diffusions consists of hyperbolic Ornstein–Uhlenbeck processes. An explicit formula for the transition density of the hyperbolic Ornstein–Uhlenbeck process is derived.

[1] A. N. Borodin, “Gipergeometricheskaya diffuziya”, Zap. nauchn. semin. POMI, 361, 2008, 29–44 | MR | Zbl

[2] A. N. Borodin, Sluchainye protsessy, Lan, S.-Peterburg, 2013

[3] J.-C. Gruet, “Windings of hyperbolic Brownian motion”, Exponential Functionals and Principal Values related to Brownian Motion, Revista Matemática Iberoamericana, Madrid, 1997, 35–42 | MR

[4] N. N. Lebedev, Spetsialnye funktsii i ikh prilozheniya, Fiz.-mat.-lit., Moskva, 1963 | MR

[5] M. Abramovits, I. Stigan, Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[6] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1974

[7] A. N. Borodin, P. Salminen, Handbook of Brownian Motion – Facts and Formulae, Second edition, Birkhäuser, Basel–Boston–Berlin, 2002 | MR | Zbl