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Exponential trends of Ornstein–Uhlenbeck first-passage-time densities

Published online by Cambridge University Press:  14 July 2016

A. G. Nobile ,
L. M. Ricciardi  and
L. Sacerdote
A. G. Nobile*
Affiliation:
University of Salerno
L. M. Ricciardi*
Affiliation:
University of Naples
L. Sacerdote*
Affiliation:
University of Salerno
*
∗Postal address: Dipartimento di Informatica e Applicazioni, Università di Salerno, 84100 Salerno, Italy.
∗∗Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy.
∗Postal address: Dipartimento di Informatica e Applicazioni, Università di Salerno, 84100 Salerno, Italy.
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Abstract

The asymptotic behaviour of the first-passage-time p.d.f. through a constant boundary for an Ornstein–Uhlenbeck process is investigated for large boundaries. It is shown that an exponential p.d.f. arises, whose mean is the average first-passage time from 0 to the boundary. The proof relies on a new recursive expression of the moments of the first-passage-time p.d.f. The excellent agreement of theoretical and computational results is pointed out. It is also remarked that in many cases the exponential behaviour actually occurs even for small values of time and boundary.

Keywords

ASYMPTOTIC BEHAVIOURFIRST-PASSAGE-TIME MOMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 360 - 369
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research carried out under CNR-JSPS Scientific Cooperation Programme, Contracts No. 83.0032.01 and No. 84.00227.01, and with MPI financial support.

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