Excessive measures and the existence of right semigroups and processes

Abstract:

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