We show that the transition p.d.f. of the Omstein-Uhlenbeck process with a reflection condition at an assigned state Sis 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 Omstein-Uhlenbeck processes.
On the probability densities of an Ornstein- Uhlenbeck process with a reflecting boundary
SACERDOTE, Laura Lea
1987-01-01
Abstract
We show that the transition p.d.f. of the Omstein-Uhlenbeck process with a reflection condition at an assigned state Sis 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 Omstein-Uhlenbeck processes.
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