Uniqueness of a martingale-coboundary decomposition of stationary processes
Samek, Pavel ; Volný, Dalibor
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 113-119 / Harvested from Czech Digital Mathematics Library
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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]).

Publié le : 1992-01-01
Classification:  28D05,  60G10 
@article{118476,
     author = {Pavel Samek and Dalibor Voln\'y},
     title = {Uniqueness of a martingale-coboundary decomposition of stationary processes},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {113-119},
     zbl = {0753.60032},
     mrnumber = {1173752},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118476}
}

Samek, Pavel; Volný, Dalibor. Uniqueness of a martingale-coboundary decomposition of stationary processes. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 113-119. http://gdmltest.u-ga.fr/item/118476/

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