Vasylyk O. Random processes from classes V(phi,psi)

The thesis is dedicated to study of analytical properties of random processes from the classes V(phi,psi). There are found conditions for boundedness and sample paths continuity with probability one of the random processes from the classes V(phi,psi) defined on compact space, and conditions, under which random processes from the classes V(phi,psi) defined on an arbitrary separable pseudometric space belong to the spaces C(T,q), as well as estimates of distributions of the norms of such processes in these spaces. Obtained results are used for studying properties of stationary random processes from the classes V(phi,psi) and processes of strictly phi-subGaussian fractional Brownian motion. There are found conditions for weak convergence of the family of random process from the class V(phi,psi) in the space C_0(R+,q) and conditions for weak convergence in the space C_0(R+,q) of some Gaussian processes to the Gaussian fractional Brownian motion. An algorithm of simulation of the phi-subGaussian generalizedfractional Brownian motion is proposed, which approximates such a process with given reliability and accuracy in C([0,1]).