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.