Author： Dedecker Jérôme
Publisher： Edp Sciences
E-ISSN： 1262-3318|5|issue|77-104
ISSN： 1292-8100
Source： ESAIM: Probability and Statistics, Vol.5, Iss.issue, 2010-03, pp. : 77-104
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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
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