Quenched Invariance Principles via Martingale ApproximationReport as inadecuate



 Quenched Invariance Principles via Martingale Approximation


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In this paper we survey the almost sure central limit theorem and its functional form quenched for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the terminology of central limit theorem and its functional form, started at a point. All these results have in common that they are obtained via a martingale approximation in the almost sure sense. We point out several applications of these results to classes of mixing sequences, shift processes, reversible Markov chains, Metropolis Hastings algorithms.



Author: Magda Peligrad

Source: https://archive.org/



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