A quenched weak invariance principle

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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  • HAL Id : hal-00713788, version 2

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Jérôme Dedecker, Florence Merlevède, Magda Peligrad. A quenched weak invariance principle. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2014, 50 (3), pp.872-898. ⟨hal-00713788v2⟩

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