A quenched weak invariance principle

2012/04/20 by Dedecker, Jérôme, Merlevède, Florence, Peligrad, Magda · 1 citation
#60F05 #60F17 #60J05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1204.4554

Abstract

In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, a theory which has interest in itself.

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• Some remarks on Gordin-Lifšic's condition for martingale approximations

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