Associated polynomials and birth-death processes

Erik A. van Doorn

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    Abstract

    We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to applications in the setting of birth-death processes. In particular, we relate the supports of the two measures, and their moments of positive and negative orders. Our results indicate how the prevalence of recurrence or $\alpha$-recurrence in a birth-death process can be recognized from certain properties of an associated measure.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2001

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1581
    ISSN (Print)0169-2690

    Keywords

    • MSC-42C05
    • EWI-3401
    • IR-65768
    • MSC-60J80

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