Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T17:58:46.072Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cogburn, R. (1962) Conditional probability operators. Ann. Math. Statist. 33, 634–658.CrossRefGoogle Scholar
Eagleson, G. K. (1974) Martingale convergence to mixtures of infinitely divisible laws. Ann. of Probability , To appear.Google Scholar
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