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Strong approximation for set-indexed partial sum processes via KMT constructions III

Published online by Cambridge University Press:  15 August 2002

E. Rio
E. Rio*
Affiliation:
Emmanuel.Rio@math.u-psud.fr
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Abstract

We generalize the results of Komlós, Major and Tusnády concerning the strong approximation of partial sums of independent and identically distributed random variables with a finite r-th momentto the case when the parameter set is two-dimensional. The most striking result is that the rates of convergence are exactly the same as in the one-dimensional case.

Keywords

Set-indexed partial-sum process / functional central limit theorem / invariance principle / strong approximation.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 319 - 338
Copyright
© EDP Sciences, SMAI, 1997

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