For a class of high-order stochastic nonlinear systems, which are neither necessarily feedback linearizable nor
affine in the control input, this paper investigates the problem of state-feedback stabilization. By using the homogeneous
domination and backstepping technique, a state-feedback controller is designed, which ensures that the closed-loop system
has an almost surely unique solution on [0,+∞), and the equilibrium of the closed-loop system is globally asymptotically
stable in probability. The main contribution lies in completely relaxing the power order restriction for high-order systems
and leads to new results. A simulation example shows the effectiveness of the state-feedback controller.