由随机过程序列产生的滑动平均过程部分和的弱收敛

Weak Convergence for Partial Sums of Moving-Average Processes Generated by Stochastic Process

本文讨论了由ρ-混合随机过程序列产生的形如Xk(t)=∑j=0∞ajεk-j(t),0≤t≤1,其中{aj;j≥0)为一实数序列,满足∑j=0∞|aj|<∞的滑动平均过程部分和的弱收敛性;同时也讨论了由此滑动平均过程产生的形如Yn(s,t)=1/n^(1/2)∑k=1[n,s]Xk(t),0≤s,t ≤ 1的随机过程的弱收敛性,以及随机足标和SNn(t)=∑k=1NnXk(t)的弱收敛性.

In this paper, we discuss weak convergence for partial sums of moving-average processes generated by ρ-mixing stochastic process of the form Xk(t) = ∑j=0∞ajεk-j(t), 0 ≤ t≤ 1, where {aj; j ≥ 0} is a sequence of real numbers with ∑j=0∞ |aj|<∞.Fur-thermore, weak convergence of stochastic process of the form Yn(s,t) =1/n^(1/2) ∑k=1[ns]Xk(t), 0 ≤ s, t ≤ 1 and weak convergence of stochastic subscript sums of SNn(t) = ∑k=1Nn Xk(t) are also discussed.