Moving Averages of Homogeneous Random Fields
Bruckner, L. A.
Ann. Math. Statist., Tome 42 (1971) no. 6, p. 2147-2149 / Harvested from Project Euclid
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Let $X(g)$ be a homogeneous random field on a discrete locally compact Abelian group $G$. Let $H(X)$ be the linear completion of $\{X(g): g \in G\}$ in $L_2$ space. The following result is obtained: there exists a fundamental random field $Y(g)$ on $G$ with values in $H(X)$ such that $X(g)$ is obtained as a moving average of $Y(g)$ if, and only if, $X(g)$ has a spectral density which is positive almost everywhere with respect to the Haar measure on the dual group of $G$.
Publié le : 1971-12-14
Classification:  
@article{1177693083,
     author = {Bruckner, L. A.},
     title = {Moving Averages of Homogeneous Random Fields},
     journal = {Ann. Math. Statist.},
     volume = {42},
     number = {6},
     year = {1971},
     pages = { 2147-2149},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177693083}
}

Bruckner, L. A. Moving Averages of Homogeneous Random Fields. Ann. Math. Statist., Tome 42 (1971) no. 6, pp.  2147-2149. http://gdmltest.u-ga.fr/item/1177693083/