  We study ergodic quadratic optimal stochastic control problems for an affine
state equation with state and control dependent noise and with stochastic
coefficients. We assume stationarity of the coefficients and a finite cost
condition. We first treat the stationary case and we show that the optimal cost
corresponding to this ergodic control problem coincides with the one
corresponding to a suitable stationary control problem and we provide a full
characterization of the ergodic optimal cost and control.
