Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T02:21:30.865Z Has data issue: false hasContentIssue false
  • English
  • Français

On the evaluation of first-passage-time probability densities via non-singular integral equations

Published online by Cambridge University Press:  01 July 2016

V. Giorno ,
A. G. Nobile ,
L. M. Ricciardi  and
S. Sato
V. Giorno*
Affiliation:
University of Salerno
A. G. Nobile*
Affiliation:
University of Salerno
L. M. Ricciardi*
Affiliation:
University of Naples
S. Sato*
Affiliation:
Osaka University
*
∗Postal address: Dipartimento di Informatica e Applicazioni, University of Salerno, 84100 Salerno, Italy.
∗Postal address: Dipartimento di Informatica e Applicazioni, University of Salerno, 84100 Salerno, Italy.
∗∗ Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy.
∗∗∗ Postal address: Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka (Osaka), Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

The algorithm given by Buonocore et al. [1] to evaluate first-passage-time p.d.f.’s for Wiener and Ornstein–Uhlenbeck processes through a time-dependent boundary is extended to a wide class of time-homogeneous one-dimensional diffusion processes. Several examples are thoroughly discussed along with some computational results.

Keywords

DIFFUSION PROCESSESVARYING BOUNDARIESRESTRICTED PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 20 - 36
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Buonocore, A., Nobile, A. G. and Ricciardi, L. M. (1987) A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Prob. 19, 784–800.Google Scholar
2. Feller, W. (1936) Zur Theorie der stochastichen Prozesse. Math. Ann. 113, 113–160.CrossRefGoogle Scholar
3. Feller, W. (1951) Two singular diffusion processes. Ann. Math. 54, 173–182.Google Scholar
4. Fortet, R. (1943) Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dérivées partielles du type parabolique. J. Math. Pures Appl. 22, 177–243.Google Scholar
5. Giorno, V., Nobile, A. G., Ricciardi, L. M. and Sacerdote, L. (1986) Some remarks on the Rayleigh process. J. Appl. Prob. 23, 398–408.Google Scholar
Gardshteyn, I. S. and Ryzhik, I. M. (1965) Tables of Integrals, Series and Products. Academic Press, New York.Google Scholar