A general martingale approach to discrete time stochastic control and estimation

A general method of constructing system models for the solution of discrete time stochastic control and estimation problems is presented. The method involves the application of modern martingale theory and entails the judicious choice of certain sigma-algebras and martingales. General estimation equations are derived for observations taking values in a countable space, and previously obtained estimation equations are exhibited as special cases. Finally, an example of the application of these methods to a stochastic control problem is analyzed.