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On Gordin's central limit theorem for stationary processes

Published online by Cambridge University Press:  14 July 2016

G. K. Eagleson
G. K. Eagleson*
Affiliation:
University of Cambridge
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Abstract

The central limit theorem for ergodic stationary processes obtained by Gordin is shown to hold for general stationary processes. In this case, the limit law is a mixture of normals.

Keywords

STATIONARY PROCESSESCENTRAL LIMIT THEOREMMIXTURES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 176 - 179
Copyright
Copyright © Applied Probability Trust 1975 

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References

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Gordin, M. I. (1969) The central limit theorem for stationary processes. (In Russian) Dokl. Akad. Nauk. S.S.S.R. 188, 739–741.Google Scholar
Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition. Proc. Nat. Acad. Sci. U.S.A. 42, 43–47.Google Scholar
Rosenblatt, M. (1971) Markov Processes. Structure and Asymptotic Behaviour. Springer-Verlag, Berlin.Google Scholar