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 probabi1ity current. Such equation, that are seen to be useful also for computationa1 purposes, yield as an immediate consequence all known closed form results for Ornstein-Uhlenbeck process.
On the probability densities of an Ornstein-Uhlenbeck process with reflecting boundaries / Ricciardi, LUIGI MARIA; L., Sacerdote. - STAMPA. - (1986), pp. 359-366.
On the probability densities of an Ornstein-Uhlenbeck process with reflecting boundaries
RICCIARDI, LUIGI MARIA;
1986
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 probabi1ity current. Such equation, that are seen to be useful also for computationa1 purposes, yield as an immediate consequence all known closed form results for Ornstein-Uhlenbeck process.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
