Strong mixing properties of linear stochastic processes

Let { Z t ; 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 { g v ; 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 { X t ; 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.) X a , ···, X b then for any where M is a finite positive constant which depends only on ϕ 0 and