Displaying similar documents to “A remark on Vapnik-Chervonienkis classes”

Bounds on regeneration times and limit theorems for subgeometric Markov chains

Randal Douc, Arnaud Guillin, Eric Moulines (2008)

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

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This paper studies limit theorems for Markov chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster–Lyapunov conditions. The regeneration-split chain method and a precise control of the modulated moment of the hitting time to small sets are employed...

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.