Let $\{Y_i;-\infty <i<\infty \}$ be a doubly infinite sequence of identically distributed and extended negatively dependent random variables with zero means and finite variance and $\{a_i;-\infty <i<\infty \}$ be an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of the moving-average process $X_k={\sum }_{i=-\infty }^{\infty }{a}_{i+k}{Y}_i,$ and extend to the m-extended negatively dependent case.

中文翻译：

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END假设下移动平均过程的完整矩收敛

让 $\{{ÿ}_{\mathrm{一世}};-\infty <\mathrm{一世}<\infty \}$ 是具有零均值和有限方差且分布相同且扩展为负相关的随机变量的双无限序列，并且 $\{{\mathrm{一种}}_{\mathrm{一世}};-\infty <\mathrm{一世}<\infty \}$是绝对可积的实数序列。在本文中，我们证明了移动平均过程的完整矩收敛性$X_{ķ}={\sum }_{\mathrm{一世}=-\infty }^{\infty }{\mathrm{一种}}_{\mathrm{一世}+ķ}{ÿ}_{\mathrm{一世}}，$并扩展到m扩展的负相关情况。