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On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes

Published online by Cambridge University Press:  22 January 2016

Izumi Kubo
Izumi Kubo*
Affiliation:
Mathematical Institute, Nagoya University
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We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 103 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Kawata, T.: On the Fourier series of a stationary process. Z. Wahrsh. 6 (1966) 224–245.CrossRefGoogle Scholar
[2] Kawata, T.: On the Fourier series of a stationary process, II. Z. Wahrsh. 12 (1969).Google Scholar
[3] Zygmund, A.: Trigonometrical series. Warszawa (1935).Google Scholar