On stochastic relaxed control for partially observed diffusions

Abstract

In this paper we are concerned with stochastic relaxed control problems of the following kind. Let X ( t ), t ≥ 0, denote the state of a process being controlled, Y ( t ), t ≥ 0, the observation process and p ( t , ·) a relaxed control, that is a process with values probability measures on the control region Г . The state and observation processes are governed by stochastic differential equations and where B and W are independent Brownian motions with values in R n and R m respectively, (put m = 1 for simplicity).

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