Equivalence of the strong Feller properties of analytic semigroups and associated resolvents

TL;DR

This paper establishes conditions under which the strong Feller property of analytic semigroups is equivalent to that of their resolvents, linking two important concepts in the analysis of Markov processes.

Contribution

It provides new sufficient conditions demonstrating the equivalence of strong Feller properties for analytic semigroups and their resolvents.

Findings

Identifies conditions for equivalence of strong Feller properties

Bridges the gap between semigroup and resolvent properties

Enhances understanding of Markov process regularity

Abstract

In this paper, we give sufficient conditions for the equivalence between semigroup strong Feller property and resolvent strong Feller property.