Concentration inequalities for dependent Random variables via the martingale method

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dc.creatorLeonid
dc.creatorKontorovich
dc.creatorRamanan, Kavita
dc.date2006-09-29
dc.date2009-01-19
dc.date.accessioned2026-07-07T12:32:40Z
dc.date.available2026-07-07T12:32:40Z
dc.descriptionThe martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, bounds are obtained on martingale differences associated with the random sequences, which may be of independent interest. As applications of the main result, concentration inequalities are also derived for inhomogeneous Markov chains and hidden Markov chains, and an extremal property associated with their martingale difference bounds is established. This work complements and generalizes certain concentration inequalities obtained by Marton and Samson, while also providing different proofs of some known results.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOP384 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0609835
dc.identifierhttp://arxiv.org/abs/math/0609835
dc.identifierAnnals of Probability 2008, Vol. 36, No. 6, 2126-2158
dc.identifierdoi:10.1214/07-AOP384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216858
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject60E15 (Primary) 60J10, 60G42 (Secondary)
dc.titleConcentration inequalities for dependent Random variables via the martingale method
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