Almost sure convergence for weighted sums of extended negatively dependent random variables
详细信息 查看全文
- 作者：J. Lita da Silva
- 关键词：weighted sum ; extended negatively dependent random variable ; strong law of large numbers ; 60F15
- 刊名：Acta Mathematica Hungarica
- 出版年：2015
- 出版时间：June 2015
- 年：2015
- 卷：146
- 期：1
- 页码：56-70
- 全文大小：659 KB
- 参考文献：1.Adler A., Rosalsky A., Taylor R. L.: Strong laws of large numbers for weighted sums of random elements in normed linear spaces. Int. J. Math. Math. Sci., 12, 507鈥?29 (1989)View Article MATH MathSciNet
2.T. 脟a千in and P. E. Oliveira, A note on weighted sums of associated random variables, Acta Math. Hungar., (2014), doi:10.鈥?007/鈥媠10474-014-0397-1 .
3.P. Chen and S. Gan, Limiting behavior of weighted sums of i.i.d. random variables, Statist. Probab. Lett., 77 (2007), 1589鈥?599.
4.Y. Chen, A. Chen and K. W. Ng, The strong law of large numbers for extended negatively dependent random variables, J. Appl. Probab., 47 (2010), 908鈥?22.
5.B. D. Choi and S. H. Sung, Almost sure convergence theorems of weighted sums of random variables, Stoch. Anal. Appl., 5 (1987), 365鈥?77.
6.Chow Y. S.: Some convergence theorems for independent random variables. Ann. Math. Stat., 37, 1482鈥?493 (1966)View Article MATH
7.Y. S. Chow and T. L. Lai, Limiting behavior of weighted sums of independent random variables, Ann. Probab., 1 (1973), 810鈥?24.
8.Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 3rd ed. Springer-Verlag (New York, 1997).
9.J. Cuzick, A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab., 8 (1995), 625鈥?41.
10.K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 11 (1983), 286鈥?95.
11.D. Li, A. Rosalsky and I. Volodin, On the strong law of large numbers for sequences of pairwise negative quadrant dependent random variables, Bull. Inst. Math. Acad. Sin. (N.S.), 1 (2006), 281鈥?05.
12.L. Liu, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett., 79 (2009), 1290鈥?298.
13.M. Lo猫ve, Probability Theory I, 4th ed. Springer-Verlag (New York, 1977).
14.P. E. Oliveira, Weighted sums of associated variables, J. Korean Statist. Soc., 41 (2012), 537鈥?42.
15.D. H. Qiu and P. Y. Chen, Limiting behavior of weighted sums of NOD random variables, J. Math. Res. Exposition, 31 (2011), 1081鈥?091.
16.S. Sawyer, Maximal inequalities of weak type, Ann. Math., 84 (1966), 157鈥?74.
17.Y. Shen, J. Yang and S. Hu, On strong law of large numbers and growth rate for a class of random variables, J. Inequal. Appl., 563 (2013), doi:10.鈥?186/鈥?029-242X-2013-563 .
18.W. F. Stout, Almost Sure Convergence, Academic Press (New York, 1974).
19.S. H. Sung, Almost sure convergence for weighted sums of i.i.d. random variables, J. Korean Math. Soc., 34 (1997), 57鈥?7.
20.R. L. Taylor, Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces, Lecture Notes in Mathematics 672, Springer-Verlag (1978).
21.H. Teicher, Almost certain convergence in double arrays, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 69 (1985), 331鈥?45.
22.R. Thrum, A remark on almost sure convergence of weighted sums, Probab. Theory Related Fields, 75 (1987), 425鈥?30.
23.X. Wang, T. C. Hu, A. Volodin and S. Hu, Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables, Comm. Statist. Theory Methods, 42 (2013), 2391鈥?401. - 作者单位：J. Lita da Silva (1)
1. Department of Mathematics and CMA, Faculty of Sciences and Technology, New University of Lisbon, Quinta da Torre, 2829-516, Caparica, Portugal - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Sciences
Mathematics - 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
- ISSN：1588-2632
文摘
For a triangular array \({\{a_{n, k}, 1 \leqq k \leqq n, n \geqq 1\}}\) of real numbers and a sequence of random variables \({\{X_{n}, n \geqq 1\}}\) conditions are given to ensure \({\sum_{k=1}^{n} a_{n,k} (X_{k} - \mathbb{E} X_{k}) \overset{\textnormal{a.s.}}{\longrightarrow} 0}\) Namely, the sequence \({\{X_{n}, n\geqq1\}}\) will be considered extended negatively dependent and either (i) stochastically dominated by a random variable X satisfying \({\mathbb{E}|X|^{p} < \infty}\) for some \({1 < p < 2}\) or (ii) identically distributed such that \({\mathbb{E}|X_{1}| < \infty}\).