Controlled random degenerate diffusions under long-run average cost

We study the ergodic control problem of degenerate random diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems, flexible manufacturing systems etc. Under a certain Liapunov type stability condition we establish the existence of an optimal control. We then study the corresponding HJB equation and establish the existence of a unique viscosity solution in a certain class. A characterization of the optimal control in terms of the unique viscosity solution is obtained

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