由φ-混合序列产生的长程相依过程的广义强逼近定理

A general strong approximation theorem for the long memory process generated by φ-mixing sequences

设{X_k;k≥1}是由X_k=∑_(i=0)~βα_iε_(k-i)所定义的滑动平均过程,其中{ε_i;-∞<i<∞}是一同分布的φ-混合相依变量序列,{α_i;i≥0}为满足条件α_i^i^(-α)l(i)的实数序列,l(i)为一缓变函数.当1/2<α<1时,{X_k;k≥1}为一长程相依过程.在Eε_0~2可能为无穷的条件下,对长程相依过程{X_k;k≥1}的部分和建立了一个更为一般性的强逼近定理.

Let {Xk;k≥1} be a moving average process defined by Xk=∑i ∞=0 aiεk-i,where {εi;-∞〈i〈∞）is a doubly infinite sequence of identically distributed φ-mixing random variables,{ai;i≥0）and l（i） is a slowly varying function. When 1/2 〈 a 〈 1, {Xk; k ≥ 1} is a long memory process. Under the assumption that Eε0 2]may be infinite, a general strong approximation theorem for partial sums of the long memory process is derived.