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Existence and Uniqueness of Q-Processes with a Given Finite -Invariant Measure

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Summary

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite -subinvariant measure m on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is -invariant on C, as well as a necessary condition for the uniqueness of such a process.
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Keywords: Q-matrix; construction theory; quasi-stationary distributions

Document Type: Research Article

Affiliations: Dept of Mathematics, University of Queensland, Australia

Publication date: March 1, 2004

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