# STRONG LAW OF LARGE NUMBERS FOR ASYMPTOTICALLY NEGATIVE DEPENDENT RANDOM VARIABLES WITH APPLICATIONS

• Accepted : 2010.10.11
• Published : 2011.01.30

#### Abstract

In this paper, we obtain the H$\{a}$jeck-R$\{e}$nyi type inequality and the strong law of large numbers for asymptotically linear negative quadrant dependent random variables by using this inequality. We also give the strong law of large numbers for the linear process under asymptotically linear negative quadrant dependence assumption.

#### Acknowledgement

Supported by : Daebul University

#### References

1. T.C.Christofides, Maximal inequalities for demimartingales and strong law of large numbers, Statist. Probab. Lett. 50 (2000) 357-363 https://doi.org/10.1016/S0167-7152(00)00116-4
2. J.Fazekas and O.Klesov, A general approach to the strong law of large numbers, Theory Probab. Appl. 45 (2001) 436-449 https://doi.org/10.1137/S0040585X97978385
3. J.Hajeck and A.Renyi, A generalization of an inequality of Kolomogorov, Acta. Math. Acad. Sci. Hungar. 6 (1955) 281-284 https://doi.org/10.1007/BF02024392
4. S.Hu and M.Hu, A general approach rate to the strong law of large numbers, Statist. Probab. Lett. 76 (2006) 843-851 https://doi.org/10.1016/j.spl.2005.10.016
5. S.Hu, X.Wang, W.Yang and T.Zhao, The Hajeck-Renyi type inequality for associated random variables, Statist. Probab. Lett. 79 (2009) 884-888 https://doi.org/10.1016/j.spl.2008.11.014
6. T.S.Kim and J.I.Baek A central limit theorem for stationary linear processes generated by linearly positively quadrant dependent process, Statist. Probab. Lett. 51 (2001) 299-305 https://doi.org/10.1016/S0167-7152(00)00168-1
7. J.Liu, S.Gan and P.Chen, The Hajeck-Renyi inequality for the NA random variables and its application, Statist. Probab. Lett. 43 (1999) 99-105 https://doi.org/10.1016/S0167-7152(98)00251-X
8. L.X.Zhang, A functional central limit theorem for asymptotically negatively dependent random fields, Acta Math. Hungar. 86 (2000) 237-259 https://doi.org/10.1023/A:1006720512467