QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models Fernández Rodríguez, Lidia De la Iglesia, Manuel D. Quasi-birth-and-death processes Multivariate orthogonal polynomials Jacobi–Koornwinder polynomials Urn models The work of the first author was partially supported by FEDER/Junta de Andalucía under the Research Project A-FQM-246-UGR20; MCIN/AEI 10.13039/501100011033 and FEDER funds by PGC2018-094932-B-I00; and IMAG-María de Maeztu Grant CEX2020-001105-M. The work of the second author was partially supported by PAPIIT-DGAPA-UNAM Grant IN106822 (México) and CONACYT Grant A1-S-16202 (México). 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. 2023-10-10T12:40:21Z 2023-10-10T12:40:21Z 2023-08-30 info:eu-repo/semantics/article Fernández, L., de la Iglesia, M.D. QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models. Mediterr. J. Math. 20, 290 (2023). [https://doi.org/10.1007/s00009-023-02486-z] https://hdl.handle.net/10481/84943 10.1007/s00009-023-02486-z eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Springer Nature