QBD Processes Associated with Jacobi–Koornwinder Bivariate Polynomials and Urn Models

Fernández Rodríguez, Lidia; De la Iglesia, Manuel D.

doi:10.1007/s00009-023-02486-z

QBD-Processes-Associated-.pdf (743.7Ko)

Identificadores

URI: https://hdl.handle.net/10481/84943

DOI: 10.1007/s00009-023-02486-z

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Editorial

Springer Nature

Materia

Quasi-birth-and-death processes

Multivariate orthogonal polynomials

Jacobi–Koornwinder polynomials

Urn models

Date

2023-08-30

Referencia bibliográfica

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]

Patrocinador

IMAG-María de Maeztu CEX2020-001105-M; Consejo Nacional de Ciencia y Tecnología A1-S-16202 CONACYT; Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México IN106822 DGAPA, UNAM; Fondo de Cooperación Internacional en Ciencia y Tecnología FONCICYT; European Regional Development Fund ERDF; Junta de Andalucía A-FQM-246-UGR20, PGC2018-094932-B-I00

Résumé

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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DMA - Artículos

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