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Approximations fortes pour des processus bivariés

Published online by Cambridge University Press:  20 November 2018

Nathalie Castelle
Nathalie Castelle*
Affiliation:
Laboratoire de Mathématiques—UMR 8628, Bât. 425, Université de Paris-Sud, 91405 Orsay Cedex, France, email: Nathalie.Castelle@math.u-psud.fr
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Résumé

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Nous établissons un résultat d’approximation forte pour des processus bivariés ayant une partie gaussienne et une partie empirique. Ce résultat apporte un nouveau point de vue sur deux théorèmes hongrois bidimensionnels établis précédemment, concernant l’approximation par un processus de Kiefer d’un processus empirique uniforme unidimensionnel et l’approximation par un pont brownien bidimensionnel d’un processus empirique uniforme bidimensionnel. Nous les enrichissons un peu et montrons que sous leur nouvelle forme ils ne sont que deux énoncés d’un même résultat.

Abstract

Abstract

We establish a strong approximation result for bivariate processes containing a Gaussian part and an empirical part. This result leads to a new point of view on two Hungarian bidimensional theorems previously established, about the approximation of an unidimensional uniform empirical process by a Kiefer process and the approximation of a bidimensional uniform empirical process by a bidimensional Brownian bridge. We enrich them slightly and we prove that, under their new fashion, they are but two statements of the same result.

Keywords

60F1760G1562G30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 3 , 01 June 2002 , pp. 533 - 553
Copyright
Copyright © Canadian Mathematical Society 2002

References

Références

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