- Recently, progress has been made on establishing the stability and performance of linear stochastic systems when they are adaptively controlled in a certainty equivalent fashion using least squares- or extended least squares-based parameter estimates. Here we provide an overview of these results. We consider first the case of white gaussian noise, where the convergence of the parameter estimates can be established for generically all systems. Then we provide an account of the stability and performance of certainty equivalent controllers for which parameter convergence has been established. Next we turn to the white non-gaussian case, and obtain upper bounds for the parameter error and the normalized prediction error. Finally we exploit these bounds for the self-tuning regulator when "b 0" is known and the delay equals one. 1990 the Indian Academy of Sciences.