Comptes Rendus
no. 3
Probability Theory
A nonadapted version of the invariance principle of Peligrad and Utev
[Version non adaptée du principe d'invariance de Peligrad et Utev]

Présenté par : Marc Yor

Dalibor Volný1
1 Laboratoire de mathématiques, Université de Rouen, technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France
Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 167-169.

Nous présentons une version non adaptée du principe d'invariance de Peligrad et Utev [M. Peligrad, S. Utev, A new maximal inequality and invariance principle for stationary sequences, Ann. Probab. 33 (2005) 798–815].

We present a nonadapted version of the invariance principle of Peligrad and Utev [M. Peligrad, S. Utev, A new maximal inequality and invariance principle for stationary sequences, Ann. Probab. 33 (2005) 798–815].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.05.024
Dalibor Volný 1

1 Laboratoire de mathématiques, Université de Rouen, technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France 
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Dalibor Volný. A nonadapted version of the invariance principle of Peligrad and Utev. Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 167-169. doi : 10.1016/j.crma.2007.05.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.024/

[1] P. Billingsley Convergence of Probability Measures, John Wiley & Sons Inc., New York, 1968

[2] I.P. Cornfeld; S.V. Fomin; Ya.G. Sinai Ergodic Theory, Die Grundlehren der Mathematischen Wissenschaften, vol. 245, Springer, Berlin, 1982

[3] C.C. Hall; P. Heyde Martingale Limit Theory and its Application, Academic Press, New York, 1980

[4] J. Klicnarová, D. Volný, An invariance principle for non adapted processes C. R. Acad. Sci. Paris, Ser. I, , 2007, in press | DOI

[5] M. Maxwell; M. Woodroofe Central limit theorems for additive functionals of Markov chains, Ann. Probab., Volume 28 (2000), pp. 713-724

[6] M. Peligrad; S. Utev A new maximal inequality and invariance principle for stationary sequences, Ann. Probab., Volume 33 (2005), pp. 798-815

[7] M. Peligrad; S. Utev; W.B. Wu A maximal Lp-inequality for stationary sequences and applications, Proc. Amer. Math. Soc., Volume 135 (2007), pp. 541-550

[8] M. Tyran-Kamińska, M. Mackey, Central limit theorem for non-invertible measure preserving maps, Colloquium Mathematicum (2007), in press

[9] D. Volný On the invariance principle and functional law of iterated logarithm for nonergodic processes, Yokohama Math. J., Volume 35 (1987), pp. 137-141

[10] D. Volný Martingale approximation of non adapted stochastic processes with nonlinear growth of variance (P. Bertail; P. Doukhan; P. Soulier, eds.), Dependence in Probability and Statistics Series, Lecture Notes in Statistics, vol. 187, 2006

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