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Issue ESAIM: PS
Volume 5, 2001
Page(s) 77 - 104
DOI 10.1051/ps:2001103

DOI: 10.1051/ps:2001103


ESAIM: P&S, September 2001, Vol. 5, pp. 77-104

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker

LSTA, Université de Paris 6, 175 rue du Chevaleret, 75013 Paris Cedex 05, France; (dedecker@ccr.jussieu.fr)

(Received April 9, 1999. Revised June 7, 2001.)

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


AMS Subject: 37A50, 60F17.

Key words: Functional central limit theorem, stationary random fields, moment inequalities, exponential inequalities, mixing, metric entropy, chaining.


© EDP Sciences, SMAI 2001


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