Geodesic
Weak Hölder convergence of processes with application to the perturbed empirical process
Applicationes Mathematicae, Tome 26 (1999) no. 1, pp. 63-83

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces $C^{α,0}_0$ is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample $(X_1,...,X_n)$ under a natural assumption about the regularity of the marginal distribution function F of the sample. In particular, when F is Lipschitz, the best possible bound α1/2 for the weak α-Hölder convergence of such processes is achieved.
DOI : 10.4064/am-26-1-63-83
Keywords: triangular functions, Schauder decomposition, Hölder space, tightness, Brownian bridge, perturbed empirical process

Djamel Hamadouche 1 ; Charles Suquet 1

1 
@article{10_4064_am_26_1_63_83,
     author = {Djamel Hamadouche and Charles Suquet},
     title = {Weak {H\"older} convergence of processes with application to the perturbed empirical process},
     journal = {Applicationes Mathematicae},
     pages = {63--83},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {1999},
     doi = {10.4064/am-26-1-63-83},
     zbl = {0998.60008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-26-1-63-83/}
}
TY  - JOUR
AU  - Djamel Hamadouche
AU  - Charles Suquet
TI  - Weak Hölder convergence of processes with application to the perturbed empirical process
JO  - Applicationes Mathematicae
PY  - 1999
SP  - 63
EP  - 83
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-26-1-63-83/
DO  - 10.4064/am-26-1-63-83
LA  - en
ID  - 10_4064_am_26_1_63_83
ER  - 
%0 Journal Article
%A Djamel Hamadouche
%A Charles Suquet
%T Weak Hölder convergence of processes with application to the perturbed empirical process
%J Applicationes Mathematicae
%D 1999
%P 63-83
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am-26-1-63-83/
%R 10.4064/am-26-1-63-83
%G en
%F 10_4064_am_26_1_63_83
Djamel Hamadouche; Charles Suquet. Weak Hölder convergence of processes with application to the perturbed empirical process. Applicationes Mathematicae, Tome 26 (1999) no. 1, pp. 63-83. doi: 10.4064/am-26-1-63-83

Cité par Sources :