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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 2, Pages 425–433
DOI: https://doi.org/10.4213/tvp66 (Mi tvp66) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Some remarks on an interpolation problem of A. M. Yaglom

L. Klotz

Universität Leipzig
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DOI: https://doi.org/10.4213/tvp66
Abstract: 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.
Received: 18.12.2001
Revised: 09.11.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 2, Pages 342–350
DOI: https://doi.org/10.1137/S0040585X97982402
Bibliographic databases:
Document Type: Article
Language: English
Citation: L. Klotz, “Some remarks on an interpolation problem of A. M. Yaglom”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 425–433; Theory Probab. Appl., 51:2 (2007), 342–350
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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