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Representations of the first hitting time density of an Ornstein-Uhlenbeck process. (English) Zbl 1083.60064

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.

MSC:

60J60 Diffusion processes
60E10 Characteristic functions; other transforms
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