A general approach to conditional strong laws of large numbers

Istvan Fazekas, Nyanga Honda Masasila

Abstract


A general tool to prove conditional strong laws of larger number is considered. It is shown that a conditional Kolmogorov type inequality implies a conditional Hajek–Renyi type inequality and this implies a strong law of large numbers. Both probability and moment inequalities are considered. Some applications are offered in the last section.

Keywords


Kolmogorov type inequality; Hajek–Renyi type inequality; strong laws of large numbers; conditional probability

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References


Etemadi, N., An elementary proof of the strong law of large numbers, Zeitschrift fur Wahrscheinlichkeitstheorie verw. Gebiete, 55 (1981), 119–122.

Fazekas, I., Klesov, O., A general approach to the strong law of large numbers, Theory Probab. Appl. 45(3) (2001), 436–449.

Majerek, D., Nowak, W., Zięba, W., Conditional strong law of large number, Int. J. Pure Appl. Math. 20(2) (2005), 143–156.

Prakasa Rao, B. L. S., Conditional independence, conditional mixing and conditional association, Ann. Inst. Statist. Math. 61 (2009), 441–460.

Seo, Hye-Young, Baek, Jong-Il, On Hajek–Renyi-type inequality for conditionally negatively associated random variables and its applications, J. Appl. Math. Inform. 30(3–4) (2012), 623–633.

Shuhe, Hu, Ming, Hu, A general approach rate to the strong law of large numbers, Statist. Probab. Lett. 76(8) (2006), 843–851.




DOI: http://dx.doi.org/10.17951/a.2024.78.1.27-35
Date of publication: 2024-07-29 22:47:27
Date of submission: 2024-07-22 17:29:00


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