Polosmak O. Wavelet expansions of random processes and their properties.

In the dissertation wavelet expansions for random processes from different spaces of random variables are investigated. Conditions under which wavelet expansions of random processes converge in mean square are obtained. Conditions for uniform convergence in probability on of wavelet expansions for random process from the different spaces are presented, namely, from Orlicz spaces, from from Orlicz spaces of exponential type, and for stationary Gaussian random process. Сonvergence rate of wavelet representation for random processes in the space is estimated. Properties of estimates of covariance function of Gaussian random process based on wavelet expansions was studied.