Abstract. We introduce the spaces of random variables D V,W . We study the conditions for the convergence of series and the distribution of the supremum of stochastic processes in these spaces.

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Abstract. Random sequences and stochastic processes belonging to the spaces D V,W are studied in the paper. Conditions for the sample continuity of such processes are found. The convergence of series of random variables belonging to the spaces D V,W are considered. Models of stochastic processes belonging to the spaces D V,W are studied. Several examples of models are given.