On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues

Yong Chen () and Jianmin Chen
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Yong Chen: Hunan University of Science and Technology
Jianmin Chen: Hunan University of Science and Technology

Journal of Theoretical Probability, 2011, vol. 24, issue 4, 928-938

Abstract: Abstract For an indecomposable 3×3 stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the 3×3 stochastic matrix in Johansen (J. Lond. Math. Soc. 8:345–351, 1974) is pointed out.

Keywords: Imbedding problem; Three-state time homogeneous Markov chains; Negative eigenvalues; 60J10; 60J27; 60J20 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0316-5

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