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The Helson-Sarason-Szegő theorem and the Abel summability of the series for the predictor


Author: Mohsen Pourahmadi
Journal: Proc. Amer. Math. Soc. 91 (1984), 306-308
MSC: Primary 60G25; Secondary 42A99
DOI: https://doi.org/10.1090/S0002-9939-1984-0740191-7
MathSciNet review: 740191
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Abstract: It is shown that the best linear least squares predictor of a stationary stochastic process has a mean Abel summable series representation in the time domain if its density satisfies the condition of the Helson-Sarason-Szego theorem. This provides an answer to an open question of Wiener and Masani (1958) in prediction theory.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0740191-7
Article copyright: © Copyright 1984 American Mathematical Society

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