Summary
Necessary and sufficient conditions are given for a 3×3 stochastic matrix to be embeddable by 6 elementary stochastic matrices (Poisson matrices). For a 3×3 embeddable matrix, a structure of the minimal Bang-Bang representation, i.e. the one that contains the smallest number of elementary matrices, is obtained. Based on the minimal Bang-Bang representation an algorithm for determining the embeddability of a 3×3 stochastic matrix is given.
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I would like to thank Søren Johansen for helpful comments and stimulating discussions on the subject of this paper
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Frydman, H. A structure of the Bang-Bang representation for 3×3 embeddable matrices. Z. Wahrscheinlichkeitstheorie verw Gebiete 53, 305–316 (1980). https://doi.org/10.1007/BF00531440
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DOI: https://doi.org/10.1007/BF00531440