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In this paper, the prescribed-time stabilization is studied for stochastic high-order nonlinear systems. Different from the previous research results on stochastic high-order nonlinear systems where only asymptotic stabilization or finite-time stabilization is considered, this paper proposes a new design to achieve stabilization in the prescribed-time. Specifically, the designed controller can ensure that the closed-loop system has an almost surely unique strong solution and the equilibrium of the closed-loop system is prescribed-time mean-square stable. The design method is verified by an example.