Abstract
The situation where a totally observed process y t is generated by a stochastic differential equation whose parameters evolve on a finite set {1, ... N} according to a stochastic differential equation is considered. The optimal control law is sought with respect to quadratic loss functions on y t and the control u t . The auxiliary P.D.E. technique of Hijab [6] is used together with a nonlinear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxiliary P.D.E. and strong solutions to the system S.D.E. under the given control inputs.
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