  We present existence and discrete-time approximation results on optimal
control policies for continuous-time stochastic control problems under a
variety of information structures. These include fully observed models,
partially observed models and multi-agent models with decentralized information
structures. While there exist comprehensive existence and approximations
results for the fully observed setup in the literature, few prior research
exists on discrete-time approximation results for partially observed models.
For decentralized models, even existence results have not received much
attention except for specialized models and approximation has been an open
problem. Our existence and approximations results lead to the applicability of
well-established partially observed Markov decision processes and the
relatively more mature theory of discrete-time decentralized stochastic control
to be applicable for computing near optimal solutions for continuous-time
stochastic control.
