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Complete moment convergence of moving average processes under \(\varphi \)-mixing assumptions. (English) Zbl 1186.60031

Summary: Let \(\{Y_i: - \infty <i<\infty \}\) be a sequence of identically distributed \(\varphi \)-mixing random variables, and \(\{a_i: - \infty <i<\infty \}\) an absolutely summable sequence of real numbers. In this work we prove the complete moment convergence for the partial sums of moving average processes \(\{X_n = \sum _{i=-\infty}^\infty a_i Y_{i+n}:n\geq 1\}\), improving the result of T. S. Kim and M. H. Ko [Statist. Probab. Lett. 78, No. 7, 839–846 (2008; Zbl 1140.60315)].

MSC:

60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks

Citations:

Zbl 1140.60315
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References:

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