Sergienko M. Majorizing measures method in the statistics of random processes.

The thesis is devoted to the study majorizing measures method and the use of this method for distribution estimates extremes of random processes with some Orlicz spaces of random variables. In the thesis investigates the basic properties of the majorizing measures method in Orlicz spaces of exponential type. This method was first comprehensively studied and applied to specific spaces and Orlicz space square-Gaussian random processes. In this paper, the majorizing measures method is used for the distribution of ratings extremes of random processes with some Orlicz space of random variables. Obviously, these estimates are obtained under some conditions on the process. In addition, if the process under investigation satisfies more restrictive conditions, then the tail of the distribution of extremes of the process is more "light". The most general conditions under which we found estimates for the distribution of the extremes of a stochastic process from an Orlicz space coincide with the known conditions of boundedness of Gaussian processes and processes from special Orlicz space. In addition, in the thesis are costructed tests for hypothesis testing concerning the correlation function of the Gaussian stationary random process. Using the theory of majorizing measures method are found conditions selective continuity with the probability one of random processes with Orlicz spaces and spaces of square-Gaussian random processes.