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May, 1984 On the Mean Convergence of the Best Linear Interpolator of Multivariate Stationary Stochastic Processes
Mohsen Pourahmadi
Ann. Probab. 12(2): 609-614 (May, 1984). DOI: 10.1214/aop/1176993308

Abstract

It is shown that a necessary and sufficient condition, for the existence of a mean-convergent series for the linear interpolator of a $q$-variate stationary stochastic process $\{X_n\}$ with density matrix $W$, is that the Fourier series of the isomorph of the linear interpolator should converge in the norm of $L^2(W)$, and this happens if the past and future of the process are at positive angle. This provides a positive answer to a question of H. Salehi (1979) concerning the square summability of the inverse of $W$ and improves upon the work of Rozanov (1960) and Salehi (1979).

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Mohsen Pourahmadi. "On the Mean Convergence of the Best Linear Interpolator of Multivariate Stationary Stochastic Processes." Ann. Probab. 12 (2) 609 - 614, May, 1984. https://doi.org/10.1214/aop/1176993308

Information

Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0531.62080
MathSciNet: MR735856
Digital Object Identifier: 10.1214/aop/1176993308

Subjects:
Primary: 62M10
Secondary: 60G12

Keywords: $q$-variate stationary processes , angle , Fourier series and coefficients , interpolator , linear interpolation , minimality , spectral density function

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 2 • May, 1984
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