Strong Law of Large Numbers for Random Variables with Superadditive Moment Function


In this paper, we study random variables with moment function of superadditive structure. We do not impose any assumptions on the structure of dependence of these random variables. We prove the strong law of large numbers for such random variables under regularly varying normalization by the method developed by Fazekas and Klesov. In this proof we use different properties of superadditive and ragularly varying functions. The key role in the proof is played by the possibility of approximating the nondifferentiable slowly varying function by differentiable slowly varying function. This result can be applied for obtaining strong law of large numbers for independent, orthogonal and stationary dependent random variables, submartingales. It can be used for obtaining an analogical result in the case of random fields.

Publication year: 
С. 39—42. Бібліогр.: 4 назви.

1. I. Fazekas and O. Klesov, “A general approach to the strong law of large numbers”, Theory Probab. Appl, vol. 45, no. 3, pp. 436—449, 2000.
2. F. Moricz, “Moment inequalities and the strong laws of large numbers”, Z. Wahrsch. Verw. Gebiete, vol. 35, pp. 299—314, 1976.
3. E. Seneta, Regularly Varying Functions. Berlin-Heidelberg- New York: Springer-Verlag, 1976.
4. Псевдорегулярні функції та узагальнені процеси відновлення / В.В. Булдигін, К.-Х. Індлекофер, О.І. Клесов, Й.Г. Штейнбах. — К.: ТВіМС, 2012. — 442 с.

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