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Complete convergence of moving average processes under dependence assumptions. (English) Zbl 0873.60019

The author considers a moving-average process \(X_k=\sum_{i=-\infty}^\infty a_{i+k}Y_i\), \(k\geq 1\), for an absolutely summable sequence \(\{a_i\}\) of real numbers and a doubly infinite sequence \(\{Y_i\}\) of identically distributed and \(\varphi\)-mixing random variables. Under a slight condition on the \(\varphi\)-mixing coefficient and \(EY_1=0\), \(E|Y_1|^{rt}<\infty\) for \(1\leq t<2\), \(r\geq 1\), the convergence of the series \(\sum_{n=1}^\infty n^{r-2}P(|\sum_{k=1}^n X_k|\geq n^{1/t}\varepsilon)\) for all \(\varepsilon>0\) could be proved.

MSC:

60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks
60G05 Foundations of stochastic processes
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