Excessive measures and the existence of right semigroups and processes. (English) Zbl 0658.60108
Under the general setting where \((U_{\alpha})\) denotes a submarkov resolvent with proper potential kernel U on a Lusin space (E,G) and the constant 1 is supposed to be \((U_{\alpha})\)-excessive, the author studies the problem of the existence of right-continuous processes (resp. semi-groups) associated with the given resolvent. Sufficient conditions for this existence theorem are the following:
Unicity principle for potential of measures; Representation as potential of excessive measures dominated by a potential; Representation of purely excessive measures by entrance laws.
A characterization of non-branching points for \((U_{\alpha})\) by means of extreme rays in the cone of excessive measures is also given. The paper would be easier to read if it were written in a more reduced length.
Unicity principle for potential of measures; Representation as potential of excessive measures dominated by a potential; Representation of purely excessive measures by entrance laws.
A characterization of non-branching points for \((U_{\alpha})\) by means of extreme rays in the cone of excessive measures is also given. The paper would be easier to read if it were written in a more reduced length.
Reviewer: X.L.Nguyen
Keywords:
submarkov resolvent; existence of right-continuous processes; Unicity principle for potential of measures; Representation as potential of excessive measures; entrance lawsReferences:
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