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In this paper, a method is given for stabilizing compensation design for a large class of discrete time nonlinear stochastic systems with incomplete state information. The nonlinearity is contained either in the state or the output equation and it involves a zero mean white noise sequence. The proposed compensator is a constant gain observer together with a constant feedback control gain. The stabilizability conditions depend on characteristics of system parameters and are for both mean square and almost surely stochastic stability of the controlled system.