Abstract
For weighted sums of sequences of asymptotically almost negatively associated (AANA) random variables, we study the complete moment convergence by using the Rosenthal type moment inequalities. Our results extend the corresponding ones for sequences of independently identically distributed random variables of Chow [4].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
An J, Complete convergence of weighted sums for sequences of AANA radom variables (submitted)
Cai G H, Complete convergence for weighted sums of sequences of AANA random variables, Glasgow Math. J. 17(1) (2004) 165–181
Chen P Y and Wang D C, Complete moment convergence for sequence of identically distributed φ-mixing random variables, Acta Math. Sin. Engl. Ser. 26(4) (2010) 679–690
Chow Y S, On the rate of moment complete convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sin. 16 (1988) 177–201
Chow Y S and Teicher H, Probability theory: independent, interchangeability, Martingales, third edition) (1997) (New York: Springer)
Chandra T K and Ghosal S, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hung. 71(4) (1996a) 327–336
Chandra T K and Ghosal S, The strong law of large numbers for weighted averages under dependence assumptions, J. Theor. Probab. 9(3) (1996b) 797–809
Ghosal S and Chandra T K, Complete convergence of martingale arrays, J. Theor. Probab. 11 (1998) 621–631
Gut A, Probability theory: a graduate course (2005) (New York: Springer)
Kim T S, Ko M H and Lee I H, On the strong laws for asymptotically almost negatively associated random variables, Rocky Mt. J. Math. 34(3) (2004) 979–989
Li Y X and Zhang L X, Complete moment convergence of moving average under dependent assumptions, Stat. Probab. Lett. 70 (2004) 191–197
Li D L, Rao B, Jiang T F and Wang X C, Complete convergence and almost sure convergence of weighted sums of random variables, J. Theor. Probab. 8 (1995) 49–76
Petrov V V, Limit theorems of probability: sequences of independent random variables (1995) (Oxford: Clarendon Press)
Wang X J, Hu S H and Yang W Z, Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables, Discret. Dyn. Nat. Soc., Article ID 717126 (2011) 11 page. doi:10.1155/2012/717126
Yang W Z, Wang X J, Ling N X and Hu S H, On complete convergence of moving average process for AANA sequence, Discret. Dyn. Nat. Soc., Article ID 86391 (2012) 24 pages. doi:10.1155/2012/863931
Yuan D M and An J, Rosenthal type inqualities for asymptotically almost negatively associated random variables and applications, Sci. China Ser. A 52(9) (2009) 1887–1904
Zhou X C and Lin J G, Complete q-moment convergence of moving average process under φ-mixing assumption, J. Math. Res. Expo. 31(4) (2011) 687–697
Acknowledgments
The author is very grateful to the anonymous referee for helpful suggestions on the original manuscript. This work is supported by the Projects of Science and Technology Research of Chongqing City Education Committee.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
AN, J. Complete moment convergence of weighted sums for processes under asymptotically almost negatively associated assumptions. Proc Math Sci 124, 267–279 (2014). https://doi.org/10.1007/s12044-014-0170-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-014-0170-y