Zhou, Xingcai Complete moment convergence of moving average processes under \(\varphi \)-mixing assumptions. (English) Zbl 1186.60031 Stat. Probab. Lett. 80, No. 5-6, 285-292 (2010). 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)]. Cited in 32 Documents MSC: 60F15 Strong limit theorems 60G50 Sums of independent random variables; random walks Citations:Zbl 1140.60315 PDFBibTeX XMLCite \textit{X. Zhou}, Stat. Probab. Lett. 80, No. 5--6, 285--292 (2010; Zbl 1186.60031) Full Text: DOI References: [1] Baek, J. I.; Kim, T. S.; Liang, H. Y., On the convergence of moving average processes under dependent conditions, Aust. N. Z. J. Stat., 45, 331-342 (2003) · Zbl 1082.60028 [2] Bai, Z. D.; Su, C., The complete convergence for partial sums of i.i.d. random variables, Sci. Sin. A, 28, 1261-1277 (1985) · Zbl 0554.60039 [3] Burton, R. M.; Dehling, H., Large deviations for some weakly dependent random processes, Statist. Probab. Lett., 9, 397-401 (1990) · Zbl 0699.60016 [4] Chen, P. Y.; Hu, T. C.; Volodin, A., Limiting behaviour of moving average processes under \(\varphi \)-mixing assumption, Statist. Probab. Lett., 79, 105-111 (2009) · Zbl 1154.60026 [5] Ibragimov, I. A., Some limit theorem for stationary processes, Theory Probab. Appl., 7, 349-382 (1962) · Zbl 0119.14204 [6] Kim, T. S.; Ko, M. H., Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett., 78, 839-846 (2008) · Zbl 1140.60315 [7] Li, D.; Rao, M. B.; Wang, X. C., Complete convergence of moving average processes, Statist. Probab. Lett., 14, 111-114 (1992) · Zbl 0756.60031 [8] Li, Y. X.; Zhang, L. X., Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett., 70, 191-197 (2004) · Zbl 1056.62100 [9] Shao, Q. M., A moment inequality and its application, Acta Math. Sin., 31, 736-747 (1988), (in Chinese) · Zbl 0698.60025 [10] Yu, D. M.; Wang, Z. J., Complete convergence of moving average processes under negative dependence assumptions, Math. Appl. (Wuhan), 15, 30-34 (2002) · Zbl 1010.62081 [11] Zhang, L., Complete convergence of moving average processes under dependence assumptions, Statist. Probab. Lett., 30, 165-170 (1996) · Zbl 0873.60019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.