Hölderian invariance principle for Hilbertian linear processes

Račkauskas, Alfredas; Suquet, Charles

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1051/ps:2008011

Title :

Hölderian invariance principle for Hilbertian linear processes

Author(s) :

Račkauskas, Alfredas [Auteur]
Department of Mathematics and Informatics [Vilnius]
Suquet, Charles [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

ESAIM: Probability and Statistics

Pages :

261-275

Publisher :

EDP Sciences

Publication date :

2009-07-04

ISSN :

1292-8100

English keyword(s) :

Mathematics

English abstract : [en]

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 ...
Show more >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 , .Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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