This paper is devoted to the study of the existence and uniqueness of the invariant measure associated to the transition semigroup of a diffusion process in a bounded open subset of Rn. For this purpose, we investigate first the invariance of a bounded open domain with piecewise smooth boundary showing that such a property holds true under the same conditions that insure the invariance of the closure of the domain. A uniqueness result for the invariant measure is obtained in the class of all probability measures that are absolutely continuous with respect to Lebesgue’s measure. A sufficient condition for the existence of such a measure is also provided.

Invariant measures associated to degenerate elliptic operators

Da Prato, Giuseppe;Cannarsa, Piermarco
2010

Abstract

This paper is devoted to the study of the existence and uniqueness of the invariant measure associated to the transition semigroup of a diffusion process in a bounded open subset of Rn. For this purpose, we investigate first the invariance of a bounded open domain with piecewise smooth boundary showing that such a property holds true under the same conditions that insure the invariance of the closure of the domain. A uniqueness result for the invariant measure is obtained in the class of all probability measures that are absolutely continuous with respect to Lebesgue’s measure. A sufficient condition for the existence of such a measure is also provided.
2010
File in questo prodotto:
File Dimensione Formato  
3886.pdf

accesso aperto

Descrizione: journal article full text
Tipologia: Altro materiale allegato
Licenza: Non pubblico
Dimensione 289.32 kB
Formato Adobe PDF
289.32 kB Adobe PDF

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: https://hdl.handle.net/11384/91989
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 6
  • OpenAlex ND
social impact