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A paper is devoted to new expansions of random processes in the form of series. In particular case the expansions in series of stationary stochastic processes with absolutely continuous spectral function and the expansions with respect to some functions which generate wavelet basis are obtained. These results are used for model construction of stochastic processes in such way that the model approximates the process with given reliability and accuracy in some Banach spaces. The conditions of uniform convergence of Gaussian random series with independent summands are also given.

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