Complete convergence of moving average processes under dependence assumptions
Complete convergence of moving average processes under dependence assumptions
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DOI：
10.1016/0167-7152(95)00215-4
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发表时间：
1996-10-15
影响因子：
0.8
通讯作者：
Zhang, LX
中科院分区：
文献类型：
--
作者：
Zhang, LX
设\(\{Y_i; -\infty < i < \infty\}\)是一列同分布且\(\varphi\)-混合的随机变量的双边无穷序列，\(\{a(i); -\infty < i < \infty\}\)是一个绝对可和的实数列。在本文中，我们在一些适当的条件下证明了\(\left\{\frac{\sum_{k = 1}^{n}\sum_{i = -\infty}^{\infty}a(i + k)Y_i}{n^{\frac{1}{t}}}; n\geq1\right\}\)的完全收敛性。
Let {Y-i; -infinity < i < infinity} be a doubly infinite sequence of identically distributed and phi-mixing random variables, {a(i); -infinity < i < infinity} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of {Sigma(k=1)(n) Sigma(i = -infinity) a(i+k)Yi/n(1/t); n greater than or equal to 1} under some suitable conditions.