QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models

2022/12/09 by Lidia Fernández, Fernández, Lidia, Manuel D. de la Iglesia +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2212.05041

openalex publication_date 2022/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of quasi-birth-and-death (QBD) processes associated with the so-called first family of Jacobi-Koornwinder bivariate polynomials. These polynomials are orthogonal on a bounded region typically known as the swallow tail. We will explicitly compute the coefficients of the three-term recurrence relations generated by these QBD polynomials and study the conditions under we can produce families of discrete-time QBD processes. Finally, we show an urn model associated with one special case of these QBD processes.

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