A separation principle for partially observed control of singular stochastic processes

The analysis of partially observed stochastic control problems often replaces the unknown state process with its conditional distribution given the observations. This technique rewrites the dynamics in terms of knowable processes whose costs coincide with the original processes. This paper considers stochastic processes having singular behavior and presents an approach which separates the determination of the optimal control from the task of estimating the conditional distribution of the unknown process. It involves using a martingale problem characterization for the dynamics followed by a further characterization using occupationmeasures. This final characterization forms the basis for an equivalent linear programming formulation of the problem over the space of occupation measures. 2005 Elsevier Ltd. All rights reserved.