no. 4
Probability Theory
Invariance principle for a class of non stationary processes with long memory
[Principe d'invariance pour des processus non stationnaires à longue mémoire]

Présenté par : Marc Yor

Philippe, Anne1 ; Surgailis, Donatas2 ; Viano, Marie-Claude3
1 Université de Nantes, laboratoire de mathématiques Jean-Leray, UMR CNRS 6629, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 3, France
2 Vilnius Institute of Mathematics and Informatics, 2600 Vilnius, Lithuania
3 Université de Lille 1, laboratoire Paul-Painlevé UMR CNRS 8524, bâtiment M2, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mathématique, Tome 342 (2006) no. 4, pp. 269-274.

Nous étudions une famille de processus non stationnaires à longue mémoire. Nous prouvons un théorème limite fonctionnel pour le processus des sommes partielles.

We prove a functional central limit theorem for the partial sums of a class of time varying processes with long memory.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.001
Philippe, Anne 1 ; Surgailis, Donatas 2 ; Viano, Marie-Claude 3

1 Université de Nantes, laboratoire de mathématiques Jean-Leray, UMR CNRS 6629, 2, rue de la Houssinière, BP 92208, 44322 Nantes cedex 3, France
2 Vilnius Institute of Mathematics and Informatics, 2600 Vilnius, Lithuania
3 Université de Lille 1, laboratoire Paul-Painlevé UMR CNRS 8524, bâtiment M2, 59655 Villeneuve d'Ascq cedex, France 
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Philippe, Anne; Surgailis, Donatas; Viano, Marie-Claude. Invariance principle for a class of non stationary processes with long memory. Comptes Rendus. Mathématique, Tome 342 (2006) no. 4, pp. 269-274. doi : 10.1016/j.crma.2005.12.001. http://www.numdam.org/articles/10.1016/j.crma.2005.12.001/

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

[2] Brockwell, P.J.; Davis, R.A. Time Series: Theory and Methods, Springer-Verlag, New York, 1991

[3] A. Philippe, D. Surgailis, M.-C. Viano, Time-varying fractionally integrated processes with nonstationary long memory, Technical report, Pub. IRMA Lille, 61(9), 2004

[4] Surgailis, D. Non-CLTs: U-statistics, multinomial formula and approximations of multiple Itô-Wiener integrals (Doukhan, P. et al., eds.), Theory and Applications of Long-Range Dependence, Birkhäuser, Boston, MA, 2003, pp. 129-142

[5] Taqqu, M.S. Fractional Brownian motion and long-range dependence (Doukhan, P. et al., eds.), Theory and Applications of Long-Range Dependence, Birkhäuser, Boston, MA, 2003, pp. 5-38

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⁎ The research is supported by joint Lithuania and France scientific program PAI EGIDE 09393 ZF.