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Zbl 1133.60314
Ditlevsen, Susanne
A result on the first-passage time of an Ornstein-Uhlenbeck process. (English)
[J] Stat. Probab. Lett. 77, No. 18, 1744-1749 (2007). ISSN 0167-7152

Summary: Consider the first time an Ornstein-Uhlenbeck process starting from zero crosses a constant positive threshold. Assuming that the asymptotic mean is above the threshold, conditions on the asymptotic variance relative to the distance between the threshold and the asymptotic mean given that ensure the finiteness of the positive Laplace transforms.
MSC 2000:
*60G15 Gaussian processes

Keywords: Laplace transform; martingales; eigenfunctions; conditional moments; Hermite polynomials

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