Regular Markov chains for which the transition matrix has large exponent
type: Item
instance of: scholarly article
title: Regular Markov chains for which the transition matrix has large exponent
zbMATH Open document ID: 0965.15026
DOI: 10.1016/S0024-3795(99)00265-7
author: S. J. Kirkland
author: M. Neumann
published in: Linear Algebra and its Applications
publication date: 2001-01-10T00:00:00Z
review text: The exponent \(\exp(T)\) of a primitive \((n\times n)\) nonnegative matrix \(T\) is the smallest positive integer \(r\) for which \(T^r\) is positive. The authors investigate, using condition numbers, the stability of the stationary distributions of \((n\times n)\) primitive stochastic matrices \(P\) for which \(\exp(P)\geq [{(n-1)^2+ 1\over 2}]+ 2\). The work is a sequel to that of \textit{S. J. Kirkland} [Linear Algebra Appl. 253, 103-112 (1997; Zbl 0878.15015)].
reviewed by: Eugene Seneta
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 1532992
zbMATH Keywords: transition matrix
zbMATH Keywords: matrix exponent
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: condition numbers
zbMATH Keywords: stability
zbMATH Keywords: primitive stochastic matrices
MaRDI profile type: Publication
cites work: Generalized inverses. Theory and applications.
cites work: Q4326384
cites work: Q4002435
cites work: Group generalized inverses of M-matrices associated with periodic and nonperiodic jacobi matrices
cites work: On the first and second order derivatives of the Perron vector
cites work: Sensitivity of the stationary distribution vector for an ergodic Markov chain
cites work: Uniform Stability of Markov Chains
cites work: Q3262596
cites work: A note on the eigenvalues of a primitive matrix with large exponent
cites work: Applications of Paz's inequality to perturbation bounds for Markov chains
cites work: A system of gaps in the exponent set of primitive matrices
cites work: The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
cites work: The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
cites work: Sensitivity of the Stationary Distribution of a Markov Chain
cites work: Perturbation of the stationary distribution measured by ergodicity coefficients
cites work: Sensitivity of finite Markov chains under perturbation
description: scientific article; zbMATH DE number 1532992