Applications of Paz's inequality to perturbation bounds for Markov chains

DOI10.1016/S0024-3795(97)00042-6zbMath0891.65147MaRDI QIDQ1375093

Michael Neumann, Bryan L. Shader, Stephen J. Kirkland

Publication date: 3 July 1998

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Markov chainscondition numberstochastic matricesperturbation bounds

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Inequalities involving eigenvalues and eigenvectors (15A42) Stochastic matrices (15B51) Probabilistic methods, stochastic differential equations (65C99)

Related Items (18)

A functional approximation for the M/G/1/N queue ⋮ Acute perturbation of the group inverse ⋮ Unnamed Item ⋮ Improved bounds for a condition number for Markov chains ⋮ On Perturbation Bounds for the Joint Stationary Distribution of Multivariate Markov Chain Models ⋮ On optimal condition numbers for Markov chains ⋮ Strong stability and perturbation bounds for discrete Markov chains ⋮ Structured perturbations of Drazin inverse ⋮ Structured perturbations of group inverse and singular linear system with index one ⋮ New perturbation bounds for denumerable Markov chains ⋮ Comparison of perturbation bounds for the stationary distribution of a Markov chain ⋮ On a bound on algebraic connectivity: the case of equality ⋮ Digraph-based conditioning for Markov chains ⋮ Mixing time estimation in reversible Markov chains from a single sample path ⋮ Markov chain sensitivity measured by mean first passage times ⋮ Regular Markov chains for which the transition matrix has large exponent ⋮ Stationary distributions and mean first passage times of perturbed Markov chains ⋮ Sharp Entrywise Perturbation Bounds for Markov Chains

Cites Work

• Sensitivity of the stationary distribution vector for an ergodic Markov chain
• Non-negative matrices and Markov chains. 2nd ed
• Comparison of eigenvectors of irreducible stochastic matrices
• On diagonal dominance arguments for bounding \(\| A^{-1}\|_\infty\)
• Entrywise perturbation theory and error analysis for Markov chains
• Sensitivity of finite Markov chains under perturbation
• Perturbation of the stationary distribution measured by ergodicity coefficients
• The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Sensitivity of the Stationary Distribution of a Markov Chain
• Uniform Stability of Markov Chains
• On a bound on algebraic connectivity: the case of equality
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