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First-passage-time density and moments of the ornstein-uhlenbeck process

Published online by Cambridge University Press:  14 July 2016

Luigi M. Ricciardi  and
Shunsuke Sato
Luigi M. Ricciardi*
Affiliation:
Università di Napoli
Shunsuke Sato*
Affiliation:
Osaka University
*
∗ Dipartimento di Matematica e Applicazioni, Universitá di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy.
∗∗ Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan 560.
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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 purposes.

Keywords

FIRST-PASSAGE-TIME PROBLEMCONSTANT BOUNDARYEXPONENTIAL TRENDSASYMPTOTIC BEHAVIOR
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 43 - 57
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research partly carried out under CNR-JSPS Scientific Cooperation Programme, contract Nos. 84.00227.01, 85.00002.01 and under MPI financial support.

References

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