Turchyn I. Convergence of stochastic processes' representations in form of wavelet-based series

Series expansions of stochastic processes are studied in the thesis. We proved theorems about expansions of stochastic processes in wavelet-based series with uncorrelated summands. We obtained conditions of uniform convergence with probability 1 for series with independent summands and conditions of uniform convergence in probability for expansions of strictly phi-sub-Gaussian stochastic processes. We obtained estimates for distributions of Gaussian stochastic processes' norms in L_p([0,T]). We studied rate of expansions' convergence in L_p([0,T]) - for phi-sub-Gaussian, strictly sub-Gaussian and Gaussian processes, and in C([0,T]) and Orlicz spaces - for strictly sub-Gaussian processes.