Geodesic
Hyperbolic Ornstein--Uhlenbeck process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 45-55

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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. 
@article{ZNSL_2015_441_a4,
     author = {A. N. Borodin},
     title = {Hyperbolic {Ornstein--Uhlenbeck} process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--55},
     publisher = {mathdoc},
     volume = {441},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a4/}
}
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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/