Exponential inequalities and functional central limit theorems for random fields
نویسنده
چکیده
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 φ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. Résumé Nous établissons des inégalités exponentielles pour des sommes partielles issues de champs aléatoires. En utilisant des arguments de châınage classiques, nous donnons ensuite des conditions suffisantes pour que des processus de sommes partielles indexés par de grandes classes d’ensembles convergent vers un mouvement Brownien. Pour les champs stationnaires de variables aléatoires bornées, la condition fait intervenir une série d’espérances conditionnelles. Dans le cas des champs non uniformément φ-mélangeants, nous supposons l’existence de moments d’ordre quatre ainsi qu’une decroissance algébrique des coefficients de mélange. Mathematics Subject Classifications (1991): 60 F 05, 60 F 17.
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