In this paper, a scheme for approximating in the mean square \linebreak the solutions of a stochastic system of differential equations with delay by the solutions of a system of stochastic differential equations without delay is proposed. Stochastic differential equations with delay play an important role in modeling real processes with memory, but their study is complicated by the infinite dimensionality of the phase space. To overcome these difficulties, we develop an approach based on approximating a system with delay by a system of ordinary differential equations of increased dimension. The main result is to prove that under certain conditions, the solutions of the approximating system coincide in the mean square to the solutions of the original system with delay. This approach allows for efficient analysis and modeling of stochastic systems with delay using finite-dimensional stochastic differential equations without delay.

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