Quasi-birth-and-death processes and multivariate orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:499

Article

Fernandez, Lidia^1,2  de la Iglesia, Manuel D.³ 

[1] Univ Granada, IEMATH GR, Granada 18071, Spain

[2] Univ Granada, Dept Matemat Aplicada, Granada 18071, Spain

[3] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

关键词: Quasi-birth-and-death processes;    Bivariate orthogonal polynomials;    Urn models;   

DOI  :  10.1016/j.jmaa.2021.125029

来源: Elsevier

【 摘 要 】

The aim of this paper is to study some models of quasi-birth-and-death (QBD) processes arising from the theory of bivariate orthogonal polynomials. First we will see how to perform the spectral analysis in the general setting as well as to obtain results about recurrence and the invariant measure of these processes in terms of the spectral measure supported on some domain Omega subset of R-d. Afterwards, we will apply our results to several examples of bivariate orthogonal polynomials, namely product orthogonal polynomials, orthogonal polynomials on a parabolic domain and orthogonal polynomials on the triangle. We will focus on linear combinations of the Jacobi matrices generated by these polynomials and produce families of either continuous or discrete-time QBD processes. Finally, we show some urn models associated with these QBD processes. (C) 2021 Elsevier Inc. All rights reserved.YYY

【 授权许可】

Free