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Strong mixing properties of linear stochastic processes

Published online by Cambridge University Press:  14 July 2016

K. C. Chanda
K. C. Chanda*
Affiliation:
Wright State University, Dayton, Ohio
*
*Now at Texas Tech. University, Lubbock, Texas.
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Abstract

Let {Zt; t = 0, ± 1, ···} be a pure white noise process with γ = E{|Z1|δ}< ∞ for some δ > 0. Assume that the characteristic function (ch.f.) ϕ0 of Z1 is Lebesgue-integrable over (—∞, ∞). Let {gv;v = 0, 1, 2, ···, g0 = 1} be a sequence of real numbers such that where λ = δ(1 + δ)−1. Define , where the identity is to be understood in the sense of convergence in distribution. Then {Xt; t = 0, ± 1, ···} is a strongly mixing stationary process in the sense that if is the σ-fìeld generated by the random variables (r.v.) Xa, ···, Xb then for any where M is a finite positive constant which depends only on ϕ0 and

Keywords

LINEAR PROCESSESPROCESSES WITHOUT SECOND ORDER PROPERTIESSTRONG MIXING CONDITION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 401 - 408
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley, New York.Google Scholar
[2] Dianada, P. H. (1953) Some probability limit theorems with statistical applications. Proc. Camb. Phil. Soc. 49, 239–246.Google Scholar
[3] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar
[4] Grenander, U. and Rosenblatt, M. (1957) Statistical Analysis of Stationary Time Series. John Wiley, New York.CrossRefGoogle Scholar
[5] Hoeffding, W. and Robbins, H. (1948) The central limit theorems for dependent random variables. Duke Math. J. 15, 773–780.CrossRefGoogle Scholar
[6] Ibragimov, I. A. (1962) Some limit theorems for stationary processes. Theor. Probability Appl. 7, 349–382.CrossRefGoogle Scholar
[7] Rozanov, Yu. A. (1967) Stationary Random Processes. Holden-Day, San Francisco.Google Scholar