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A quenched weak invariance principle

Jérôme Dedecker, Florence Merlevède, Magda Peligrad (2014)

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

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 nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.

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