The ODE method for stability of skip-free Markov chains with applications to MCMC

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dc.creatorFort, Gersende
dc.creatorMeyn, Sean
dc.creatorMoulines, Eric
dc.creatorPriouret, Pierre
dc.date2006-07-31
dc.date2008-04-02
dc.date.accessioned2026-07-07T09:29:44Z
dc.date.available2026-07-07T09:29:44Z
dc.descriptionFluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this paper, some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time, space and the initial condition by a large constant. The resulting fluid limit is the solution of an ordinary differential equation (ODE) in ``most'' of the state space. Stability and finer ergodic properties for the stochastic model then follow from stability of the set of fluid limits. Moreover, similarly to the queueing context where fluid models are routinely used to design control policies, the structure of the limiting ODE in this general setting provides an understanding of the dynamics of the Markov chain. These results are illustrated through application to Markov chain Monte Carlo methods.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP471 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0607800
dc.identifierhttp://arxiv.org/abs/math/0607800
dc.identifierAnnals of Applied Probability 18, 2 (2008) 664-707
dc.identifierdoi:10.1214/07-AAP471
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157894
dc.subjectProbability
dc.subject60J10, 65C05 (Primary)
dc.titleThe ODE method for stability of skip-free Markov chains with applications to MCMC
dc.typetext

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