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Zbl 1083.60064
Alili, L.; Patie, P.; Pedersen, J.L.
Representations of the first hitting time density of an Ornstein-Uhlenbeck process. (English)
[J] Stoch. Models 21, No. 4, 967-980 (2005). ISSN 1532-6349; ISSN 1532-4214/e

The paper provides three representations for the first hitting time density of the Ornstein-Uhlenbeck process. The first one is a series expansion involving the eigenvalues of a Sturm-Liouville boundary problem associated with the Laplace transform of the first hitting time. The second one is an integral representation involving Hermite functions. The third one is expressed in terms of a functional of a 3-dimensional Bessel bridge. The authors also discuss how the three representations can be used to obtain numerical approximations for the first hitting time density, and provide computational results showing high accuracy of the approximation methods.
[Alexander Mitrophanov (Atlanta)]

MSC 2000:: *60J60 Diffusion processes
60E10 Transforms of probability distributions

Keywords: Bessel bridge; Fourier transform; Laplace transform

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