[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2018.31.1.343

THE COMPLETE CONVERGENCE FOR DEPENDENT RANDOM VARIABLES IN HILBERT SPACES

Kim, Hyun-Chull (Department of Mathematics Education Sehan University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.31, no.3, 2018 , pp. 343-352 More about this Journal

Abstract

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$ -mixing random variables in Hilbert spaces.

Keywords

complete convergence; negative associated random variables; ${\phi}$ -mixing random variables; Hilbert space; weakly upper bounded;

Citations & Related Records

Reference

1	M. H. Ko, T. S. Kim, and K. H. Han, A note on the almost sure convergence for dependent random variables in a Hilbert space, J. Theoret. Probab. 22 (2009), 506-513. DOI
2	J. J. Liu, P. Y. Chen, and S. X. Gan, The laws of large numbers for ${\phi}$ -mixing sequences, (Chiness) J. Math. (Wuhan), 18 (1998), 91-95.
3	Y. Miao, Hajeck-Renyi inequality for dependent random variables in Hilbert space and applications, Revista De La Union Mathematica Argentina, 53 (2012), no. 1, 101-112.
4	L. V. Thanh, On the almost sure convergence for dependent random vectors in Hilbert spaces, Acta. Math. Hungar. 139 (2013), 276-285. DOI
5	L. X. Zhang, Strassen's law of the iterated logarithm for negatively associated random vectors, Stoch. Process. Appl. 95 (2001), no. 2, 311-328. DOI
6	P. Billingsley, Convergence of probability measures, John Wiley and Sons. Inc. New York, 1968.
7	A. Gut, Complete convergence for arrays, Period. Math. Hungar. 25 (1992), 51-75. DOI
8	N. T. T. Hien and L. V. Thanh, On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces, Statist. Probab. Lett. 107 (2015), 236-245. DOI
9	N. V. Huan, On the complete convergence for sequences of random vectors in Hilbert spaces, Acta Math. Hungar. 147 (2015), no. 1, 205-219. DOI
10	N. V. Huan, N. V. Quang, and N. T. Thuan, Baum-Katz type theorems for coordinatewise negatively associated random vectors in Hilbert spaces, Acta. Math. Hungar. 144 (2014), no. 1, 132-149. DOI
11	I. A. Ibragimov and Y. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971.
12	K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Stat. 11 (1983), 286-295. DOI