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Excessive measures and Markov processes with random birth and death. (English) Zbl 0584.60085
Summary: Given an excessive measure $$\eta$$ for a right Markov semigroup $$(P_ t)$$, one can construct a stationary strong Markov process with $$\eta$$ as one-dimensional distribution and with $$(P_ t)$$ as transition semigroup. This process has random birth and death times and the underlying measure space may have infinite mass. The process, whose construction follows easily from a theorem of Kuznetsov, leads to new interpretations of various Riesz type decompositions of the measure $$\eta$$ and of the Hunt balayage of $$\eta$$ on a set. In addition, it allows one to consider the nontransient case and to provide a last exit type decomposition of $$\eta$$.

##### MSC:
 60J45 Probabilistic potential theory
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##### References:
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