First-passage-time density and moments of the ornstein-uhlenbeck process
- 1 March 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (1) , 43-57
- https://doi.org/10.2307/3214232
Abstract
A detailed study of the asymptotic behavior of the first-passage-time p.d.f. and its moments is carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant boundary. Explicit expressions are determined which include those earlier discussed by Sato [15] and by Nobile et al. [9]. In particular, it is shown that the first-passage-time p.d.f. can be expressed as the sum of exponential functions with negative exponents and that the latter reduces to a single exponential density as time increases, irrespective of the chosen boundary. The explicit expressions obtained for the first-passage-time moments of any order appear to be particularly suitable for computation purposesKeywords
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