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

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.
24
355
369
Diffusion process; reflecting boundary; absorbing boundary; Ornstein Uhlenbeck process
RICCIARDI L.M.; L. SACERDOTE
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/9682
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact