Zatula D. Estimates for the distribution of Holder semi-norms of random processes and their applications

The thesis is devoted to estimates of the distributions of some functionals of random processes, in particular, estimates for the distributions of Holder semi-norms of random processes from F_psi(Omega) and L_p(Omega) spaces, defined on a compact or an infinite interval, and also improving results for processes from Orlicz spaces are obtained. On the basis of obtained estimations the moduli of continuity and conditions under which the Holder condition satisfies for above processes were found. Basing on obtained estimates, theorems on accuracy and reliability of approximation of processes from F_psi(Omega) and L_p(Omega) spaces, defined on an infinite interval, were proved using entire functions of exponential type.