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.

Potential-theoretical methods in the construction of measure-valued Markov branching processes

“…According to Corollary 3.6 from [18], it will be sufficient to prove that the uniqueness of charges and the specific solidity of potentials hold for U β .…”

Measure-valued discrete branching Markov processes

“…We proceed as in the proof of Proposition 4.5 from [4]. According to Corollary 3.6 from [33], it will be sufficient to prove that the uniqueness of charges and the specific solidity of potentials properties hold for…”

“…Remark 2.2. (i) Condition (h1) is necessary in order to deduce that U is the resolvent family of a (Borel) right process; see [31], [33], [5], and [8].…”