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On the equivalence of [mu]-invariant measures for the minimal process and its q-matrix



In this paper we obtain necessary and sufficient conditions for a measure or vector that is [mu]-invariant for a q-matrix, Q, to be [mu]-invariant for the family of transition matrices, {P(t)}, of the minimal process it generates. Sufficient conditions are provided in the case when Q is regular and these are shown not to be necessary. When [mu]-invariant measures and vectors can be identified, they may be used, in certain cases, to determine quasistationary distributions for the process.

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