Grozian T.M.

Estimates for Moments of Extreme Values of the Random Process with Superadditive Moment Function

This paper considers the stochastic process with superadditive moment function. The aim is to generalize the results of R. Serfling, which he received for a sequence of random variables with superadditive moment function. We have obtained the estimation for moments of supremum of a random process with the appropriate bounds for moments of this random process. We make no assumptions about the structure of the dependence of increments of a random process, but only the estimation for moments of random process.

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.