Abstract
We give a characterization of the eigenvalues of Markov operators which admit an orthogonal polynomial basis as eigenfunctions, in the Hermite and the Laguerre cases, as well as for the sequences of orthogonal polynomials associated to some probability measures on ℕ. In the Hermite case, we also give a description of the path of the associated Markov processes, as well as a geometric interpretation.
Keywords
- Probability Measure
- Orthogonal Polynomial
- Hermite Polynomial
- Jacobi Polynomial
- Laguerre Polynomial
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© 2003 Springer-Verlag Berlin Heidelberg
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Bakry, D., Mazet, O. (2003). Characterization of Markov semigroups on ℝ Associated to Some Families of Orthogonal Polynomials. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_2
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DOI: https://doi.org/10.1007/978-3-540-40004-2_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20520-3
Online ISBN: 978-3-540-40004-2
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