Comparison between criteria leading to the weak invariance principle

Olivier Durieu; Dalibor Volný

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 2, page 324-340
  • ISSN: 0246-0203

Abstract

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The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28 (2000) later improved upon by Peligrad and Utev in Ann. Probab.33(2005). We prove that in every ergodic dynamical system with positive entropy, if we consider two of these criteria, we can find a function in 𝕃 2 satisfying the first but not the second.

How to cite

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Durieu, Olivier, and Volný, Dalibor. "Comparison between criteria leading to the weak invariance principle." Annales de l'I.H.P. Probabilités et statistiques 44.2 (2008): 324-340. <http://eudml.org/doc/77972>.

@article{Durieu2008,
abstract = {The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28 (2000) later improved upon by Peligrad and Utev in Ann. Probab.33(2005). We prove that in every ergodic dynamical system with positive entropy, if we consider two of these criteria, we can find a function in $\mathbb \{L\}^\{2\}$ satisfying the first but not the second.},
author = {Durieu, Olivier, Volný, Dalibor},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stationary process; central limit theorem; weak invariance principle; martingale approximation; projective criterion},
language = {eng},
number = {2},
pages = {324-340},
publisher = {Gauthier-Villars},
title = {Comparison between criteria leading to the weak invariance principle},
url = {http://eudml.org/doc/77972},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Durieu, Olivier
AU - Volný, Dalibor
TI - Comparison between criteria leading to the weak invariance principle
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 2
SP - 324
EP - 340
AB - The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincaré Probab. Statist.36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab.28 (2000) later improved upon by Peligrad and Utev in Ann. Probab.33(2005). We prove that in every ergodic dynamical system with positive entropy, if we consider two of these criteria, we can find a function in $\mathbb {L}^{2}$ satisfying the first but not the second.
LA - eng
KW - stationary process; central limit theorem; weak invariance principle; martingale approximation; projective criterion
UR - http://eudml.org/doc/77972
ER -

References

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