Abstract: This paper investigates the problem of output-feedback control for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique, introducing a new rescaling transformation, and choosing an appropriate Lyapunov function, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. Furthermore, we address the problem of inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the design.