Constructing Markov Processes with Random Times of Birth and Death

  • R. K. Getoor
  • Joseph Glover
Part of the Progress in Probability and Statistics book series (PRPR, volume 13)


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.


Markov Process Inverse Limit Finite Measure Transition Semigroup Excessive Measure 
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Copyright information

© Birkhäuser Boston 1987

Authors and Affiliations

  • R. K. Getoor
    • 1
  • Joseph Glover
    • 2
  1. 1.Department of Mathematics, C-012University of CaliforniaLa JollaUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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