Excessive Measures and the Existence of Right Semigroups and Processes

Abstract

ABSTRACT. Given a resolvent (Un) on a Lusin space (E. IE) , the paper gives necessary and sufficient conditions in terms of the excessive measures that ensure the existence of a right process, resp. a right continuous semigroup, on (E. IE) with resolvent (Un). Furthermore, a notion of nonbranch points with respect to (U,,) is introduced-also in terms of the excessive measures-and various characterizations are given. They show, in particular, the equivalence of this definition with those introduced and discussed by Engelbert and Wittmann.