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Exponential inequalities and functional central limit theorems for random fields

Published online by Cambridge University Press:  15 August 2002

Jérôme Dedecker
Jérôme Dedecker*
Affiliation:
LSTA, Université de Paris 6, 175 rue du Chevaleret, 75013 Paris Cedex 05, France; dedecker@ccr.jussieu.fr.
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Abstract

We establish new exponential inequalities for partial sums of random fields. Next, using classicalchaining arguments, we give sufficient conditions for partial sum processes indexed by large classes ofsets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, thecondition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixingrandom fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients.

Keywords

Functional central limit theoremstationary random fieldsmoment inequalitiesexponential inequalitiesmixingmetric entropychaining.

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 77 - 104
Copyright
© EDP Sciences, SMAI, 2001

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