An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes

Takehiko Morita

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Uniqueness of a martingale-coboundary decomposition of stationary processes

Pavel Samek, Dalibor Volný (1992)

Commentationes Mathematicae Universitatis Carolinae

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In the limit theory for strictly stationary processes $f \circ T^{i}, i \in ℤ$ , the decomposition $f = m + g - g \circ T$ proved to be very useful; here $T$ is a bimeasurable and measure preserving transformation an $(m \circ T^{i})$ is a martingale difference sequence. We shall study the uniqueness of the decomposition when the filtration of $(m \circ T^{i})$ is fixed. The case when the filtration varies is solved in [13]. The necessary and sufficient condition of the existence of the decomposition were given in [12] (for earlier and weaker versions of the results...