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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 2, Pages 425–433 (Mi tvp66)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

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

L. Klotz

Universität Leipzig

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.

DOI: https://doi.org/10.4213/tvp66

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English version:
Theory of Probability and its Applications, 2007, 51:2, 342–350

Bibliographic databases:

Received: 18.12.2001
Revised: 09.11.2005
Language:

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 articles:
    1. Heo J., “Stochastic Processes and Spectral Analysis For Hilbert C-Module-Valued Maps”, Bull. Malays. Math. Sci. Soc., 41:1 (2018), 191–206  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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