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A control scheme is presented for effective stabilization of discrete-time, nonlinear stochastic systems where the nonlinearity involves a zero-mean, independent random sequence. The control is of a constant feedback type and makes use of finite time solutions of a Riccati-like matrix difference equation. Stability results are both in terms of mean square and almost sure stochastic stability. Moreover, a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem.