[For the entire collection see Zbl 0607.00014.]
Markov processes with random birth and death, constructed from an excessive measure and a transition semigroup, have practically become a standard tool in the theory of Markov processes. S. E. Kuznetsov gave a Kolmogorov-type construction in Teor. Veroyatn. Primen. 18, 596- 601 (1973; Zbl 0296.60049); a different construction under duality hypotheses appears in the reviewer’s paper, Z. Wahrscheinlichkeitstheor. Verw. Geb. 47, 139-156 (1979; Zbl 0406.60067).
In the paper under review, the authors offer a new construction for right processes based on the decomposition of the excessive measure into an invariant measure plus the integral of an entrance law. Their proof uses an inverse limit theorem for \(\sigma\)-finite measures, and is presented for the general situation of an entrance rule together with a nontime- homogeneous transition semigroup.