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Some remarks on the Rayleigh process

Published online by Cambridge University Press:  14 July 2016

V. Giorno,
A. G. Nobile,
L. M. Ricciardi and
L. Sacerdote
V. Giorno*
Affiliation:
University of Salerno
A. G. Nobile*
Affiliation:
University of Salerno
L. M. Ricciardi*
Affiliation:
University of Naples
L. Sacerdote*
Affiliation:
University of Turin
*
∗ Postal address: Dipartimento di Informatica e Applicazioni, Facoltà de Scienze, Università, 84100 Salerno, Italy.
∗ Postal address: Dipartimento di Informatica e Applicazioni, Facoltà de Scienze, Università, 84100 Salerno, Italy.
∗∗ Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy.
∗∗∗ Postal address: Dipartimento di Matematica, Università di Torino, Via Principe Amadeo 8, 10123 Torino, Italy.
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Abstract

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

Keywords

BESSEL PROCESSFIRST-PASSAGE TIMECONTINUOUS-STATE BRANCHINGDIFFUSION

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986, pp. 398 - 408
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research carried out under CNR–JNPS Scientific Cooperation Programme, Contracts 83.00032.01 and 84.00227.01, and under MPI support.

References

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