Abstract
Kuznetsov [11] (see also [12]) introduced a Kolmogorov-type construction in which he constructs a stationary measure Qm from a transition semigroup Pt(x,dy) and an excessive measure m. In fact, his theorem has other interesting consequences outside of the Markovian framework, but we do not discuss these here. While Kuznetsov’s proof is “elementary”, it is rather involved. The purpose of this paper is to give an alternate construction of Qm in the case of right processes. We consider both the time homogeneous and time inhomogeneous cases. Our construction does not extend to cover the other interesting cases of Kuznetsov’s theorem, but our approach may yield some insight into the measures Qm and may aid the reader interested in recent articles [5,10] in which the measure Qm has played an important role. Mitro [13] has obtained a result similar to ours under duality hypotheses on the underlying processes, but her construction is quite different from ours.
Research supported by NSF Grant DMS-8419377.
Research supported by NSF Grant DMS-8318204 and AFOSR Grant 85-0330.
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© 1987 Birkhäuser Boston
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Getoor, R.K., Glover, J. (1987). Constructing Markov Processes with Random Times of Birth and Death. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1986. Progress in Probability and Statistics, vol 13. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6751-2_5
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DOI: https://doi.org/10.1007/978-1-4684-6751-2_5
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