Comptes Rendus
Probability Theory
A nonadapted version of the invariance principle of Peligrad and Utev
[Version non adaptée du principe d'invariance de Peligrad et Utev]
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
@article{CRMATH_2007__345_3_167_0,
     author = {Dalibor Voln\'y},
     title = {A nonadapted version of the invariance principle of {Peligrad} and {Utev}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {167--169},
     publisher = {Elsevier},
     volume = {345},
     number = {3},
     year = {2007},
     doi = {10.1016/j.crma.2007.05.024},
     language = {en},
}
TY  - JOUR
AU  - Dalibor Volný
TI  - A nonadapted version of the invariance principle of Peligrad and Utev
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 167
EP  - 169
VL  - 345
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2007.05.024
LA  - en
ID  - CRMATH_2007__345_3_167_0
ER  - 
%0 Journal Article
%A Dalibor Volný
%T A nonadapted version of the invariance principle of Peligrad and Utev
%J Comptes Rendus. Mathématique
%D 2007
%P 167-169
%V 345
%N 3
%I Elsevier
%R 10.1016/j.crma.2007.05.024
%G en
%F CRMATH_2007__345_3_167_0
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

Cité par Sources :

Commentaires - Politique