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We study ergodic quadratic optimal stochastic control problems for an affinestate equation with state and control dependent noise and with stochasticcoefficients. We assume stationarity of the coefficients and a finite costcondition. We first treat the stationary case and we show that the optimal costcorresponding to this ergodic control problem coincides with the onecorresponding to a suitable stationary control problem and we provide a fullcharacterization of the ergodic optimal cost and control.

Ergodic Optimal Quadratic Control for an Affine Equation with Stochastic and Stationary Coefficients