the process with orthogonal increments

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.