Applications of Paz's inequality to perturbation bounds for Markov chains
type: Item
instance of: scholarly article
title: Applications of Paz's inequality to perturbation bounds for Markov chains
zbMATH Open document ID: 0891.65147
DOI: 10.1016/S0024-3795(97)00042-6
author: M. Neumann
author: Bryan L. Shader
author: S. J. Kirkland
published in: Linear Algebra and its Applications
publication date: 1998-07-03T00:00:00Z
review text: Let \(T\) and \(T+E\) be two \(n\times n\) nonnegative stochastic irreducible transition matrices for Markov processes whose stationary distribution vectors are \(\pi\) and \(\tilde \pi\), resp. The total error \(|\pi - \tilde \pi|_\infty\) and the relative errors \(|(\pi_j - \tilde \pi_j)/\pi_j|\) of the components can be estimated in terms of the disturbance \(E\) with coefficients which represent a sort of 'condition number' of \(A\). Using an inequality of \textit{A. Paz} [Introduction to probabilistic automata (1971; Zbl 0234.94055), Chapter IIa] the authors improve known estimates of this kind. The improvement is roughly by a factor of 2.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1100494
zbMATH Keywords: Markov chains
zbMATH Keywords: stochastic matrices
zbMATH Keywords: perturbation bounds
zbMATH Keywords: condition number
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1100494