负相依样本平滑移动过程的完全收敛性(英文)

Complete Convergence of Moving Average Processes under Negative Dependence Assumptions

设 {Yi;-∞ <i <∞ }为一负相伴的同分布随机变量序列 ,{ai;-∞ <i <∞ }为绝对可和的实数序列 .本文在适当的条件下 ,证明了平滑移动过程∑nk =1∑ ∞i=-∞ai+kYi/n1/t;n≥ 1

Let {Y i;-∞<i<∞} be a doubly infinite sequence of identically distributed and negatively associated random variables, {a i;-∞<i<∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of ∑ n k=1∑ ∞ i=-∞a i+kY i/n 1/t;n≥1 under some suitable conditions.