A quenched weak invariance principle

Jérôme Dedecker; Florence Merlevède; Magda Peligrad

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 3, page 872-898
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Dedecker, Jérôme, Merlevède, Florence, and Peligrad, Magda. "A quenched weak invariance principle." Annales de l'I.H.P. Probabilités et statistiques 50.3 (2014): 872-898. <http://eudml.org/doc/272070>.

@article{Dedecker2014,
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 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.},
author = {Dedecker, Jérôme, Merlevède, Florence, Peligrad, Magda},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {quenched central limit theorem; weak invariance principle; strong mixing; Markov chains},
language = {eng},
number = {3},
pages = {872-898},
publisher = {Gauthier-Villars},
title = {A quenched weak invariance principle},
url = {http://eudml.org/doc/272070},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Dedecker, Jérôme
AU - Merlevède, Florence
AU - Peligrad, Magda
TI - A quenched weak invariance principle
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 3
SP - 872
EP - 898
AB - 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.
LA - eng
KW - quenched central limit theorem; weak invariance principle; strong mixing; Markov chains
UR - http://eudml.org/doc/272070
ER -

References

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