In this paper, we continue the study of the class of hypergeometric diffusions started by the author. A broad subclass of these diffusions consists of hyperbolic Ornstein–Uhlenbeck processes. An explicit formula for the transition density of a hyperbolic Ornstein–Uhlenbeck process is derived. Bibliography: 7 titles.
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A. N. Borodin, “Hypergeometric diffusion,” Zap. Nauchn. Semin. POMI, 361, 29–44 (2008).
A. N. Borodin, Stochastic Processes [in Russian], Lan’, St.Petersburg (2013).
J.-C. Gruet, “Windings of hyperbolic Brownian motion,” in: M. Yor (ed.), Exponential Functionals and Principal Values Related to Brownian Motion, Revista Matemática Iberoamericana, Madrid (1997), pp. 35–72.
N. N. Lebedev, Special Functions and Their Applications, Dover, New York (1972).
M. Abramowitz and I. A. Stegun, Mathematical Functions, Dover, New York (1972).
H. Bateman and A. Erdélyi, Higher transcendental functions, Vol. 2, McGraw-Hill Book Company, Inc., New York (1956).
A. N. Borodin and P. Salminen, Handbook of Brownian Motion – Facts and Formulae, 2nd corrected ed., Birkhäuser, Basel, Heidelberg, New York, Dordrecht, London (2015).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 441, 2015, pp. 45–55.
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Borodin, A.N. Hyperbolic Ornstein–Uhlenbeck Process. J Math Sci 219, 631–638 (2016). https://doi.org/10.1007/s10958-016-3135-0
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DOI: https://doi.org/10.1007/s10958-016-3135-0