Hölderian invariance principle for Hilbertian linear processes

Alfredas Račkauskas (1, 2) , Charles Suquet (3)

1 Department of Mathematics and Informatics [Vilnius]
2 Institute of Mathematics and Informatics
3 LPP - Laboratoire Paul Painlevé - UMR 8524

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: Mathematics

Alfredas Račkauskas, Charles Suquet. Hölderian invariance principle for Hilbertian linear processes. ESAIM: Probability and Statistics, 2009, 13, pp.261-275. ⟨10.1051/ps:2008011⟩. ⟨hal-00497326⟩