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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{|Z 1 | δ}< ∞ for some δ > 0. Assume that the characteristic function (ch.f.) ϕ 0 of Z 1 is Lebesgue-integrable over (—∞, ∞). Let {gv ;v = 0, 1, 2, ···, g 0 = 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 ϕ 0 and

Keywords

LINEAR PROCESSESPROCESSES WITHOUT SECOND ORDER PROPERTIESSTRONG MIXING CONDITION

Information

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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