Stochastic processes with orthogonal polynomial eigenfunctions |
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Authors: | Bob Griffiths |
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Affiliation: | Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK |
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Abstract: | Markov processes which are reversible with either Gamma, Normal, Poisson or Negative Binomial stationary distributions in the Meixner class and have orthogonal polynomial eigenfunctions are characterized as being processes subordinated to well-known diffusion processes for the Gamma and Normal, and birth and death processes for the Poisson and Negative Binomial. A characterization of Markov processes with Beta stationary distributions and Jacobi polynomial eigenvalues is also discussed. |
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Keywords: | 33C45 60J60 60J75 |
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