zbMATH — the first resource for mathematics

On complete convergence for arrays of rowwise weakly dependent random variables. (English) Zbl 1251.60025
Summary: Some sufficient conditions for complete convergence for arrays of rowwise $$\tilde \rho$$-mixing random variables are presented without the assumption of identical distributions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of $$\tilde \rho$$-mixing random variables is obtained.

MSC:
 60F15 Strong limit theorems
Full Text:
References:
 [1] Cheng, P.E., A note on strong convergence rates in nonparametric regression, Statistics & probability letters, 24, 357-364, (1995) · Zbl 0835.62046 [2] Bai, Z.D.; Cheng, P.E.; Zhang, C.H., An extension of the hardy – littlewood strong law, Statistica sinica, 7, 923-928, (1997) · Zbl 1067.60501 [3] Cuzick, J., A strong law for weighted sums of i.i.d. random variables, Journal of theoretical probability, 8, 625-641, (1995) · Zbl 0833.60031 [4] Bai, Z.D.; Cheng, P.E., Marcinkiewicz strong laws for linear statistics, Statistics & probability letters, 46, 105-112, (2000) · Zbl 0960.60026 [5] Bradley, R.C., On the spectral density and asymptotic normality of weakly dependent random fields, Journal of theoretical probability, 5, 355-374, (1992) · Zbl 0787.60059 [6] Bryc, W.; Smolenski, W., Moment conditions for almost sure convergence of weakly correlated random variables, Proceedings of the American mathematical society, 119, 2, 629-635, (1993) · Zbl 0785.60018 [7] Peligrad, M.; Gut, A., Almost sure results for a class of dependent random variables, Journal of theoretical probability, 12, 87-104, (1999) · Zbl 0928.60025 [8] Utev, S.; Peligrad, M., Maximal inequalities and an invariance principle for a class of weakly dependent random variables, Journal of theoretical probability, 16, 1, 101-115, (2003) · Zbl 1012.60022 [9] Gan, S.X., Almost sure convergence for $$\widetilde{\rho}$$-mixing random variable sequences, Statistics & probability letters, 67, 289-298, (2004) · Zbl 1043.60023 [10] Kuczmaszewska, A., On chung – teicher type strong law of large numbers for $$\widetilde{\rho}$$-mixing random variables, Discrete dynamics in nature and society, 2008, 10, (2008), Article ID 140548 · Zbl 1145.60308 [11] Wu, Q.Y.; Jiang, Y.Y., Some strong limit theorems for $$\widetilde{\rho}$$-mixing sequences of random variables, Statistics & probability letters, 78, 8, 1017-1023, (2008) · Zbl 1148.60020 [12] Cai, G.H., Strong law of large numbers for $$\widetilde{\rho}$$-mixing sequences with different distributions, Discrete dynamics in nature and society, 2006, 7, (2006), Article ID 27648 [13] Cai, G.H., Marcinkiewicz strong laws for linear statistics of $$\widetilde{\rho}$$-mixing sequences of random variables, Annals of the Brazilian Academy of sciences, 78, 4, 615-621, (2006) · Zbl 1147.60310 [14] Kuczmaszewska, A., On complete convergence for arrays of rowwise dependent random variables, Statistics & probability letters, 77, 11, 1050-1060, (2007) · Zbl 1120.60025 [15] Zhu, M.H., Strong laws of large numbers for arrays of rowwise $$\widetilde{\rho}$$-mixing random variables, Discrete dynamics in nature and society, 2007, 6, (2007), Article ID 74296 · Zbl 1181.60044 [16] An, J.; Yuan, D.M., Complete convergence of weighted sums for $$\widetilde{\rho}$$-mixing sequence of random variables, Statistics & probability letters, 78, 12, 1466-1472, (2008) · Zbl 1155.60316 [17] Sung, S.H., Complete convergence for weighted sums of $$\widetilde{\rho}$$-mixing random variables, Discrete dynamics in nature and society, 2010, 13, (2010), Article ID 630608 [18] Peligrad, M., Maximum of partial sums and an invariance principle for a class of weak dependent random variables, Proceedings of the American mathematical society, 126, 4, 1181-1189, (1998) · Zbl 0899.60044 [19] Budsaba, K.; Chen, P.; Volodin, A., Limiting behavior of moving average processes based on a sequence of $$\rho^-$$-mixing random variables, Thailand Statistician, 5, 69-80, (2007) · Zbl 1143.62050 [20] Budsaba, K.; Chen, P.; Volodin, A., Limiting behavior of moving average processes based on a sequence of $$\rho^-$$-mixing and NA random variables, Lobachevskii journal of mathematics, 26, 17-25, (2007) · Zbl 1132.60028
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.