Displaying similar documents to “Bounds on regeneration times and limit theorems for subgeometric Markov chains”

On the discrepancy of Markov-normal sequences

M. B. Levin (1996)

Journal de théorie des nombres de Bordeaux

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We construct a Markov normal sequence with a discrepancy of O ( N - 1 / 2 log 2 N ) . The estimation of the discrepancy was previously known to be O ( e - c ( log N ) 1 / 2 ) .

On convergence of homogeneous Markov chains

Petr Kratochvíl (1983)

Aplikace matematiky

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Let p t be a vector of absolute distributions of probabilities in an irreducible aperiodic homogeneous Markov chain with a finite state space. Professor Alladi Ramakrishnan conjectured the following strict inequality for norms of differences p t + 2 - p t + 1 < p t + 1 - p t . In the paper, a necessary and sufficient condition for the validity of this inequality is proved, which may be useful in investigating the character of convergence of distributions in Markov chains.

Moderate deviations for stationary sequences of bounded random variables

Jérôme Dedecker, Florence Merlevède, Magda Peligrad, Sergey Utev (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.