Quasi-Birth-and-Death Processes and Matrix-Valued Orthogonal Polynomials

DOI10.1137/080742816zbMath1210.60076OpenAlexW2049521134MaRDI QIDQ3079745

Aubrey Clayton

Publication date: 2 March 2011

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080742816

zbMATH Keywords

Markov chainsquasi-birth-and-death processmatrix-valued orthogonal polynomialsblock-tridiagonal matrixKarlin-McGregor representation

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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ONE-DIMENSIONAL QUANTUM WALKS WITH ONE DEFECT ⋮ Geršgorin-type and Brauer-type eigenvalue localization sets of stochastic matrices ⋮ A Geršgorin-type eigenvalue localization set with \(n\) parameters for stochastic matrices ⋮ Quasi-birth-and-death processes and multivariate orthogonal polynomials ⋮ QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models ⋮ A modification of eigenvalue localization for stochastic matrices ⋮ On the subcritical birth-and-death processes in a random environment ⋮ Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations ⋮ Birth-death chains on a spider: spectral analysis and reflecting-absorbing factorization

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