Perturbed Markov chains

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Research , Report 01 Mar 2003Embargo end date: 01 Jan 2003 English Publisher:Cambridge University Press (CUP)Journal:Journal of Applied Probability, volume 40, pages 107-122 (issn: 0021-9002, eissn: 1475-6072,

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Authors: Eilon Solan; Nicolas Vieille;

doi: 10.1239/jap/1044476830 , 10.1017/s0021900200022294 , 10.48550/arxiv.math/0306248

arXiv: math/0306248

handle: 10419/221691

Perturbed Markov chains

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Abstract

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

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Keywords

Markov chains, ddc:330, Probability (math.PR), exit distribution, [SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco, Perturbed Markov chains, Markov chains (discrete-time Markov processes on discrete state spaces), stationary distribution, perturbed markov chains; conductance, Large deviations, sensitivity analysis, 60J10; 60F10, FOS: Mathematics, 60J10, stability of a Markov chain, Mathematics - Probability, conductance, perturbation theory, 60F10, jel: jel:C44

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