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On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary

Published online by Cambridge University Press:  14 July 2016

L. M. Ricciardi  and
L. Sacerdote
L. M. Ricciardi*
Affiliation:
University of Naples
L. Sacerdote*
Affiliation:
University of Turin
*
∗Postal address: Dipartimento di Matematica e Applicazioni, University of Naples, Via Mezzocannone 8, 80134 Naples, Italy.
∗∗Postal address: Dipartimento di Matematica, University of Turin, Via Principe Amedeo 8, 10123 Turin, Italy.
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Abstract

We show that the transition p.d.f. of the Ornstein–Uhlenbeck process with a reflection condition at an assigned state S is related by integral-type equations to the free transition p.d.f., to the transition p.d.f. in the presence of an absorption condition at S, to the first-passage-time p.d.f. to S and to the probability current. Such equations, which are also useful for computational purposes, yield as an immediate consequence all known closed-form results for Wiener and Ornstein–Uhlenbeck processes.

Keywords

DIFFUSION PROCESSESWIENER PROCESSFIRST-PASSAGE TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 355 - 369
Copyright
Copyright © Applied Probability Trust 1987 

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