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.
On the probability densities of an Ornstein-Uhlenbeck process with reflecting boundaries / Ricciardi, LUIGI MARIA; L., Sacerdote. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 24:2(1987), pp. 355-369. [10.2307/3214260]
On the probability densities of an Ornstein-Uhlenbeck process with reflecting boundaries
RICCIARDI, LUIGI MARIA;
1987
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
