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• W2759694554 abstract "In this paper we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for transferring from the martingale to the original process the conditional functional central limit theorem. The condition found is simple and well adapted to a variety of examples, leading to a better understanding of the structure of several stochastic processes and their asymptotic behavior. The approximation brings together many disparate examples in probability theory. It is valid for classes of variables defined by familiar projection conditions such as Maxwell-Woodroofe condition, various classes of mixing processes including the large class of strongly mixing processes and for additive functionals of Markov chains with normal or symmetric Markov operators." @default.
• W2759694554 created "2017-10-06" @default.
• W2759694554 creator A5070400326 @default.
• W2759694554 creator A5071302362 @default.
• W2759694554 date "2009-10-19" @default.
• W2759694554 modified "2023-09-26" @default.
• W2759694554 title "On the functional CLT via martingale approximation" @default.
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