Summary
Let C n =C n (T) be the Fourier coefficients of a continuous weakly stationary process over (−1/2T,1/2T). We make some corrections of the results on the magnitude of
, in the author's previous work. We discuss in this connection about the periodicity and non-periodicity properties of weakly stationary processes. We also discuss the approximate Fourier series which approximates the given weakly stationary process and using some results on it we give a sufficient condition for the sample continuity of a weakly stationary process which is an improvement of a result of Crámer and Leadbetter.
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References
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This work was supported by NSF Grant-6175.
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Kawata, T. On the Fourier series of a stationary process. II. Z. Wahrscheinlichkeitstheorie verw Gebiete 13, 25–38 (1969). https://doi.org/10.1007/BF00535795
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DOI: https://doi.org/10.1007/BF00535795