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arXiv · 2212.05041

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

Lidia Fernández·Manuel D. de la Iglesia
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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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Lidia Fernández, Manuel D. de la Iglesia. 2022-12-09. QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models. https://arxiv.org/abs/2212.05041

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