A quenched weak invariance principle

Jérôme Dedecker (1) , Florence Merlevède (2) , Magda Peligrad (3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 Department of Mathematical Sciences [Cincinnati]

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.

Mots clés: quenched central limit theorem; weak invariance principle; Markov chains

Domaines: Probabilités [math.PR]

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