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On a number of poisson matrices in Bang-Bang representations for 3 - 3 embeddable matrices

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  • Frydman, Halina

Abstract

We give a counterexample to the Strong Bang-Bang Conjecture according to which any 3 - 3 embeddable matrix can be expressed as a product of six Poisson matrices. We exhibit a 3 - 3 embeddable matrix which can be expressed as a product of seven but not six Poisson matrices. We show that an embeddable 3 - 3 matrix P with det can be expressed as a product of at most six Poisson matrices and give necessary and sufficient conditions for a 3 - 3 stochastic matrix P with det to be embeddable. For an embeddable 3 - 3 matrix P with det we give a new bound for the number of Poisson matrices in its Bang-Bang representation.

Suggested Citation

  • Frydman, Halina, 1983. "On a number of poisson matrices in Bang-Bang representations for 3 - 3 embeddable matrices," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 464-472, September.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:3:p:464-472
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    Cited by:

    1. Jia, Chen, 2016. "A solution to the reversible embedding problem for finite Markov chains," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 122-130.

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