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Let (Xi) be a stationary process adapted to a filtration , E(Xi)=0, ; by we denote the partial sums and . Wu and Woodroofe [Wei Biao Wu, M. Woodroofe, Martingale approximation for sums of stationary processes, Ann. Probab. 32 (2004) 1674-1690] have shown that if then there exists an array of...
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