On the equivalence of μ-invariant measures for the minimal process and its q-matrix |
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收稿时间: | 1985-09-06 |
On the equivalence of μ-invariant measures for the minimal process and its q-matrix |
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Affiliation: | Department of Applied Mathematics, The University of Adelaide, G.P.O. Box 498, Adelaide, SouthAustralia |
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Abstract: | In this paper we obtain necessary and sufficient conditions for a measure or vector that is μ-invariant for a q-matrix, Q, to be μ-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 μ-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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