Soit le processus polygonal de sommes partielles bâti sur le processus linéaire , , les étant des éléments aléatoires i.i.d., centrés d’un espace de Hilbert séparable et les ’s des opérateurs linéaires bornés , vérifiant . Nous étudions le théorème limite central fonctionnel pour dans les espaces de Hölder de fonctions vérifiant uniformément en , où , avec et à variation lente. Nous prouvons la convergence en loi dans de vers un mouvement brownien à valeurs dans , sous la condition optimale que pour tout , quand tend vers l’infini, au prix dans le cas limite d’une légère restriction sur . Notre résultat s’applique en particulier au cas , .
Let be the polygonal partial sums processes built on the linear processes , , where are i.i.d., centered random elements in some separable Hilbert space and the ’s are bounded linear operators , with . We investigate functional central limit theorem for in the Hölder spaces of functions such that uniformly in , where , with and slowly varying at infinity. We obtain the weak convergence of to some valued brownian motion under the optimal assumption that for any , when tends to infinity, subject to some mild restriction on in the boundary case . Our result holds in particular with the weight functions , .
Mots clés : central limit theorem in Banach spaces, Hölder space, functional central limit theorem, linear process, partial sums process
@article{PS_2009__13__261_0, author = {Ra\v{c}kauskas, Alfredas and Suquet, Charles}, title = {H\"olderian invariance principle for hilbertian linear processes}, journal = {ESAIM: Probability and Statistics}, pages = {261--275}, publisher = {EDP-Sciences}, volume = {13}, year = {2009}, doi = {10.1051/ps:2008011}, mrnumber = {2528083}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2008011/} }
TY - JOUR AU - Račkauskas, Alfredas AU - Suquet, Charles TI - Hölderian invariance principle for hilbertian linear processes JO - ESAIM: Probability and Statistics PY - 2009 SP - 261 EP - 275 VL - 13 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2008011/ DO - 10.1051/ps:2008011 LA - en ID - PS_2009__13__261_0 ER -
%0 Journal Article %A Račkauskas, Alfredas %A Suquet, Charles %T Hölderian invariance principle for hilbertian linear processes %J ESAIM: Probability and Statistics %D 2009 %P 261-275 %V 13 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2008011/ %R 10.1051/ps:2008011 %G en %F PS_2009__13__261_0
Račkauskas, Alfredas; Suquet, Charles. Hölderian invariance principle for hilbertian linear processes. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 261-275. doi : 10.1051/ps:2008011. http://www.numdam.org/articles/10.1051/ps:2008011/
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