QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models
Classical Analysis and ODEs
2022-12-13 v2 Probability
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.
Cite
@article{arxiv.2212.05041,
title = {QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models},
author = {Lidia Fernández and Manuel D. de la Iglesia},
journal= {arXiv preprint arXiv:2212.05041},
year = {2022}
}
Comments
14 pages, 3 figures. arXiv admin note: text overlap with arXiv:2002.04536