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Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution

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, 84000 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, 84000 Salerno, Italy.
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Abstract

The asymptotic behavior of the first-passage-time p.d.f. through a constant boundary is studied when the boundary approaches the endpoints of the diffusion interval. We show that for a class of diffusion processes possessing a steady-state distribution this p.d.f. is approximately exponential, the mean being the average first-passage time to the boundary. The proof is based on suitable recursive expressions for the moments of the first-passage time.

Keywords

PASSAGE-TIME MOMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 611 - 618
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research carried out under CNR-JSPS Scientific Cooperation Programme, Contracts 83.0032.01 and 84.00227.01, and with M.P.I. financial support.

References

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[3] Nobile, A. G., Ricciardi, L. M. and Sacerdote, L. (1985) Exponential trends of Ornstein–Uhlenbeck first passage time densities. J. Appl. Prob. 22, 360–369.CrossRefGoogle Scholar
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