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On Zhao-Woodroofe’s condition for martingale approximation

By Jana Klicnarová and Dalibor Volný


The Zhao-Woodroofe condition has been introduced in [19] and it is a necessary and sufficient condition for the existence of a martingale approximation of a causal stationary process. Here, a nonadapted version is given and the convergence of Cesaro averages is replaced by a convergence of a subsequence. The nonadapted version is of a different form than in other cases, e.g. of Wu-Woodroofe or Maxwell-Woodroofe conditions ([10], [18], [15])

Topics: stationary process, martingale approximation, nonadapted version. AMS MSC 2010, 60G10
Year: 2013
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