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On an integral equation for first-passage-time probability densities

Published online by Cambridge University Press:  14 July 2016

L. M. Ricciardi
Affiliation:
Unioersitd di Napoli
L. Sacerdote
Affiliation:
Unioersitd di Salerno
S. Sato
Affiliation:
Uniuersitd di Napoli

Abstract

We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel and right-hand term are probability currents. For the case of the standard Wiener process this equation is solved in closed form not only for the class of boundaries already introduced by Park and Paranjape [15] but also for all boundaries of the type S(I) = a + bt ‘/p (p ∼ 2, a, b E ∼) for which no explicit analytical results have previously been available.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

On leave of absence from the Faculty of Engineering Science, Osaka University.

References

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