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Characterization by orthogonal polynomial systems of finite Markov chains

  • E. Seneta (a1)


The paper characterizes matrices which have a given system of vectors orthogonal with respect to a given probability distribution as its right eigenvectors. Results of Hoare and Rahman are unified in this context, then all matrices with a given orthogonal polynomial system as right eigenvectors under the constraint a 0j = 0 for j ≥ 2 are specified. The only stochastic matrices P = {pij } satisfying p 00 + p 01 = 1 with the Hahn polynomials as right eigenvectors have the form of the Moran mutation model.


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1 Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email:


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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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