Excessive measures and the existence of right semigroups and processes

Abstract

Given a resolvent ( U α ) ({U_\alpha }) on a Lusin space ( E , E ) (E,\mathfrak {E}) , 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 , E ) (E,\mathfrak {E}) with resolvent ( U α ) ({U_\alpha }) . Furthermore, a notion of nonbranch points with respect to ( U α ) ({U_\alpha }) 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.