期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
期号：2
页码：731-766
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Let T be an ergodic automorphism of the d-dimensional torus Td, andf be a continuous function from Td to R`. On the probability space Td equippedwith the Lebesgue-Haar measure, we prove the weak convergence of the sequentialempirical process of the sequence (f Ti)i1 under some mild conditions on themodulus of continuity of f. The proofs are based on new limit theorems, on newinequalities for non-adapted sequences, and on new estimates of the conditionalexpectations of f with respect to a natural ltration.
关键词：Empirical distribution function; Kiefer process; Ergodic automor-;phisms of the torus; Moment inequalities.
