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Characterization of Markov semigroups on ℝ Associated to Some Families of Orthogonal Polynomials

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1832)

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

  • eBook Packages: Springer Book Archive