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 . The estimation of the discrepancy was previously known to be .
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 . The estimation of the discrepancy was previously known to be .
Petr Kratochvíl (1983)
Aplikace matematiky
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Let 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 . 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.
Peter J. Bickel, Ya'acov Ritov, Tobias Rydén (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Petr Mandl (1979)
Banach Center Publications
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Eddy Mayer-Wolf, Alexander Roitershtein, Ofer Zeitouni (2004)
Annales de l'I.H.P. Probabilités et statistiques
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I. Koźniewska (1958)
Colloquium Mathematicae
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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.