Some bivariate stochastic models arising from group representation theory

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

de la Iglesia, Manuel D.¹  Roman, Pablo² 

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Ciudad De Mexico 04510, Mexico

[2] Univ Nacl Cordoba, CIEM, FAMAF, Medina Allende S-N Ciudad Univ, Cordoba, Argentina

关键词: Quasi-birth-and-death processes;    Switching diffusions;    Matrix-valued orthogonal polynomials;    Wright-Fisher models;   

DOI  :  10.1016/j.spa.2017.10.017

来源: Elsevier

【 摘 要 】

The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching diffusion processes), while the second component (phase) will always be discrete and finite. The infinitesimal operators of these processes will be now matrix-valued (either a block tridiagonal matrix or a matrix-valued second-order differential operator). The matrix-valued spherical functions associated to the compact symmetric pair (SU(2) x SU(2), diag SU(2)) will be eigenfunctions of these infinitesimal operators, so we can perform spectral analysis and study directly some probabilistic aspects of these processes. Among the models we study there will be rational extensions of the one-server queue and Wright-Fisher models involving only mutation effects. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free