Geodesic
Uniqueness of a martingale-coboundary decomposition of stationary processes
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 113-119.

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In the limit theory for strictly stationary processes $f\circ T^i, i\in\Bbb Z$, 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 see [7]).
Classification : 28D05, 60G10
Keywords: strictly stationary process; approximating martingale; coboundary 
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Samek, Pavel; Volný, Dalibor. Uniqueness of a martingale-coboundary decomposition of stationary processes. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 113-119. http://geodesic.mathdoc.fr/item/CMUC_1992__33_1_a12/