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Characterization by orthogonal polynomial systems of finite Markov chains
- Part of
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- Journal:
- Journal of Applied Probability / Volume 38 / Issue A / 2001
- Published online by Cambridge University Press:
- 14 July 2016, pp. 42-52
- Print publication:
- 2001
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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 a0j = 0 for j ≥ 2 are specified. The only stochastic matrices P = {pij} satisfying p00 + p01 = 1 with the Hahn polynomials as right eigenvectors have the form of the Moran mutation model.
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 