zbMATH — the first resource for mathematics

Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables. (English) Zbl 1102.60023
Summary: We establish a Rosenthal-type inequality of the maximum of partial sums for \(\rho^-\)-mixing random fields. As its applications we get the Hájek-Rényi inequality and weak convergence of sums of \(\rho^-\)-mixing sequence. These results extend related results for NA sequences and \(\rho^*\)-mixing random fields.

60F05 Central limit and other weak theorems
60E15 Inequalities; stochastic orderings
Full Text: DOI
[1] Zhang, L. X., Wang, X. Y.: Convergence rates in the strong laws of asymptotically negatively associated random fields. Appl. Math. J. Chinese Univ., 14(4), 406–416 (1999) · Zbl 0952.60031
[2] Zhang, L. X.: A functional central limit theorem for asymptotically negatively dependent random fields. Acta Math. Hungar., 86(3), 237–259 (2000) · Zbl 0964.60035
[3] Zhang, L. X.: Central limit theorems for asymptotically negatively associated random fields. Acta Math. Sinica, English Series., 16(4), 691–710 (2000) · Zbl 0977.60020
[4] Joag Dev, K., Proschan, F.: Negative Association of Random Variables with Applications. Ann. Statist., 11, 268–295 (1983) · Zbl 0508.62041
[5] Bradley, R. C.: On the spectral density and asymptotic normality of weakly dependent random fields. J. Theoret. Probab., 5, 355–373 (1992) · Zbl 0787.60059
[6] Peligrad, M., Gut, A.: Almost-sure results for a class of dependent random variables. J. Theoret. Probab., 12(1), 87–103 (1999) · Zbl 0928.60025
[7] Utev, S., Peligrad, M.: Maximal inequalities and an invariance principle for a class of weakly dependent random variables. J. Theoret. Probab., 16(1), 101–115 (2003) · Zbl 1012.60022
[8] Zhang, L. X.: Convergence rates in the strong laws of nonstationary {\(\rho\)}*ixing random fields. Acta Math. Scientia , Ser. B, 20, 303–312 (2000) (in Chinese) · Zbl 0966.60030
[9] Matula, P.: A note on the almost sure convergence of negatively deoendent variables. Statist. Probab. Lett., 15, 209–213 (1992) · Zbl 0925.60024
[10] Liu, J. J., Gan, S. X., Chen, P. Y.: The Hájeck–Rányi inequality for the NA random variables and its application. Statist. Probab. Lett., 99–105 (1999) · Zbl 0929.60020
[11] Zhang, L. X., Wen, J. W.: A weak convergence for negatively associated fields. Statist. Probab. Lett., 53, 259–267 (2001) · Zbl 0994.60026
[12] Su, C., Zhao, L. C., Wang, Y. B.: The moment inequality for the NA random variables and the weak convergence. Sci. China, Ser. A, 26, 1091–1099 (in Chinese)
[13] Patrick, B.: Convergence of Probability Measures, Wiley, New York, 1999 · Zbl 0944.60003
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.