Wu, Yongfeng; Wang, Chunhua; Volodin, Andrei Limiting behavior for arrays of rowwise \(\rho^\ast\)-mixing random variables. (English) Zbl 1283.60053 Lith. Math. J. 52, No. 2, 214-221 (2012). Summary: We study the limiting behavior of maximal partial sums for arrays of rowwise \(\rho^\ast\)-mixing random variables and obtain some new results that improve the corresponding theorem of M.-H. Zhu [Discrete Dyn. Nat. Soc. 2007, Article ID 74296, 6 p. (2007; Zbl 1181.60044)]. Cited in 11 Documents MSC: 60F15 Strong limit theorems 60F25 \(L^p\)-limit theorems Keywords:complete convergence; complete moment convergence; \(L^q\) convergence; \(\rho^\ast\)-mixing random variables Citations:Zbl 1181.60044 PDFBibTeX XMLCite \textit{Y. Wu} et al., Lith. Math. J. 52, No. 2, 214--221 (2012; Zbl 1283.60053) Full Text: DOI References: [1] R.C. Bradley, Equivalent mixing conditions for random fields, Technical report No. 336, Center for Stochastic Processes, Dept. Statistics, Univ. North Carolina, Chapel Hill, 1990. [2] Y.S. Chow, On the rate of moment complete convergence of sample sums and extremes, Bull. Inst. Math., Acad. Sin., 16:177–201, 1988. · Zbl 0655.60028 [3] P.L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Natl. Acad. Sci. USA, 33(2):25–31, 1947. · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25 [4] C.C. Moore, The degree of randomness in a stationary time series, Ann. Math. Stat., 34:1253–1258, 1963. · Zbl 0121.36302 · doi:10.1214/aoms/1177703860 [5] S. Utev and M. Peligrad, Maximal inequalities and an invariance principle for a class of weakly dependent random variables, J. Theor. Probab., 16(1):101–115, 2003. · Zbl 1012.60022 · doi:10.1023/A:1022278404634 [6] M.H. Zhu, Strong laws of large numbers for arrays of rowwise {\(\rho\)} *-mixing random variables, Discrete Dyn. Nat. Soc., 2007, Article ID 74296, 6 pp., 2007. · Zbl 1181.60044 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.