In this paper we study a class of elliptic second-order differential operators on finite dimensional convex compact sets whose principal part degenerates on a subset of the boundary of the domain. We show that the closures of these operators generate Feller semigroups. Moreover, we approximate these semigroups by iterates of suitable positive linear operators which we also introduce and study in this paper for the first time, and which we refer to as modified Bernstein-Schnabl operators. As a consequence of this approximation we investigate some regularity properties preserved by the semigroup. Finally, we consider the special case of the finite dimensional simplex and the well-known Wright-Fisher diffusion model of gene frequency used in population genetics.

Degenerate elliptic operators, Feller semigroups and modified Bernstein-Schnabl operators

ALTOMARE, Francesco;CAPPELLETTI MONTANO, MIRELLA;DIOMEDE, Sabrina
2011-01-01

Abstract

In this paper we study a class of elliptic second-order differential operators on finite dimensional convex compact sets whose principal part degenerates on a subset of the boundary of the domain. We show that the closures of these operators generate Feller semigroups. Moreover, we approximate these semigroups by iterates of suitable positive linear operators which we also introduce and study in this paper for the first time, and which we refer to as modified Bernstein-Schnabl operators. As a consequence of this approximation we investigate some regularity properties preserved by the semigroup. Finally, we consider the special case of the finite dimensional simplex and the well-known Wright-Fisher diffusion model of gene frequency used in population genetics.
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: https://hdl.handle.net/11586/130626
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact