Sensitivity of finite Markov chains under perturbation

DOI10.1016/0167-7152(93)90011-7zbMath0777.60065OpenAlexW2106967042MaRDI QIDQ1802441

Eugene Seneta

Publication date: 15 December 1993

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(93)90011-7

zbMATH Keywords

stochastic matricesergodicity coefficientunique stationary distributionrelative sensitivity factor under perturbation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stochastic matrices (15B51)

Related Items (20)

Response operators for Markov processes in a finite state space: radius of convergence and link to the response theory for axiom A systems ⋮ Approximating physical invariant measures of mixing dynamical systems in higher dimensions ⋮ Applications of Paz's inequality to perturbation bounds for Markov chains ⋮ Acute perturbation of the group inverse ⋮ Sensitivity analysis of discrete Markov chains via matrix calculus ⋮ Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes ⋮ Unnamed Item ⋮ Sensitivity of the stationary distributions of denumerable Markov chains ⋮ Improved bounds for a condition number for Markov chains ⋮ Perturbation analysis of continuous‐time absorbing Markov chains ⋮ The spectral gap and perturbation bounds for reversible continuous-time Markov chains ⋮ On the Variances and Convariances of the Duration State Sizes of Semi-Markov Systems ⋮ New perturbation bounds for denumerable Markov chains ⋮ Comparison of perturbation bounds for the stationary distribution of a Markov chain ⋮ Markov chains: ergodicity in time-discrete cases ⋮ Response and sensitivity using 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

Cites Work

• Unnamed Item
• Sensitivity of the stationary distribution vector for an ergodic Markov chain
• Explicit forms for ergodicity coefficients and spectrum localization
• Non-negative matrices and Markov chains. 2nd ed
• Perturbation of the stationary distribution measured by ergodicity coefficients
• Finite Continuous Time Markov Chains
• Coefficients of ergodicity: structure and applications
• Discrete Dynamic Programming
• Perturbation theory and finite Markov chains

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