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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We consider a random process Y (t) = exp{X(t)}, where X(t) is a centered secondorder process which correlation function R(t, s) can be represented as R u(t, y)u(s, y)dy. A multiplicative wavelet-based representation is found for Y (t).We propose a model for simulation of the process Y (t) and find its rates of convergence to the process in the spacesis a strictly sub-Gaussian process.

There has been obtained an expansion of a second-order stochastic process into a system of wavelet-based functions. This expansion is used for simulation of a sub-Gaussian stochastic process with given accuracy and reliability.