Applied Mathematics and Optimization, Vol.49, No.3, 217-239, 2004
Control with partial observations and an explicit solution of Mortensen's equation
We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function space.
Keywords:stochastic control;partial observations;filtering;recursive stochastic equations;Komlos theorem;Mortensen equation