Sufficient conditions for the existence of Feller semigroups
type: Item
instance of: scholarly article
title: Sufficient conditions for the existence of Feller semigroups
zbMATH Open document ID: 0898.47031
DOI: 10.1007/BF02320372
published in: Mathematical Notes
publication date: 1998-11-02T00:00:00Z
review text: The problem of the existence of nonnegative contraction semigroups for one-dimensional diffusion processes with nonlocal boundary conditions was considered by W. Feller. A. D. Ventsel' proved that if a second-order elliptic differential operator is the infinitesimal generator of a Feller semigroup, then its domain consists of functions satisfying nonlocal boundary conditions. Sufficient conditions for the elliptic operator with such a domain to be the infinitesimal generator of a Feller semigroup were studied in other papers. In these papers, it was assumed that the order of the nonlocal terms is lower than that of the boundary operator. The most difficult case in which the boundary and the nonlocal operators are of the same order was first considered by A. L. Skubachevskii under the condition that the nonlocal terms decrease near the boundary. We obtain sufficient conditions for the existence of Feller semigroups assuming that the condition of decreasing of the nonlocal terms may be violated near some subset of the boundary.
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 1158912
zbMATH Keywords: nonnegative contraction semigroups
zbMATH Keywords: one-dimensional diffusion processes with nonlocal boundary conditions
zbMATH Keywords: second-order elliptic differential operator
zbMATH Keywords: infinitesimal generator of a Feller semigroup
zbMATH Keywords: order of the nonlocal terms
zbMATH Keywords: decreasing of the nonlocal terms
author: Evgeny Galakhov
MaRDI profile type: Publication
cites work: The parabolic differential equations and the associated semigroups of transformation
cites work: Q4040288
description: scientific article; zbMATH DE number 1158912