Geodesic
Some remarks on an interpolation problem of A. M. Yaglom
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 425-433 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the problem of best mean-square interpolation of a continuous $q$-variate weakly stationary random process $\textbf x$ over $\mathbf R$ on the basis of the values $x_k$, $k\in\mathbf Z$, which was studied first by A. M. Yaglom [Uspehi Matem. Nauk (N.S.), 4 (1949), pp. 173–178] in the case $q=1$. For the family $\mathscr J_\mathbf{Z}$ of all subsets of $\mathbf R$ which are shifts of $\mathbf Z$, criterions of $\mathscr J_\mathbf Z$-singularity and $\mathscr J_\mathbf Z$-regularity in terms of the nonstochastic spectral measure of $\mathbf x$ are given. Related results for stationary sequences over $\mathbf Z$ are stated.
Keywords: $q$-variate weakly stationary process, best mean-square interpolation, $\mathscr J$-regularity and $\mathscr J$-singularity, linear filtration. 
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L. Klotz. Some remarks on an interpolation problem of A. M. Yaglom. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 425-433. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a13/

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