ERGODIC BOUNDARY POINT CONTROL OF STOCHASTIC SEMILINEAR SYSTEMS/

A controlled Markov process in a Hilbert space and an ergodic cost fun ctional are given for a control problem that is solved where the proce ss is a solution of a parameter-dependent semilinear stochastic differ ential equation and the control can occur only on the boundary or at d iscrete points in the domain. The linear term of the semilinear differ ential equation is the infinitesimal generator of an analytic semigrou p. The noise for the stochastic differential equation can be distribut ed, boundary and point. Some ergodic properties of the controlled Mark ov process are shown to be uniform in the control and the parameter. T he existence of an optimal control is verified to solve the ergodic co ntrol problem. The optimal cost is shown to depend continuously on the system parameter.