The value function in ergodic control of diffusion processes with partial observations -II

Abstract

The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equiv- alent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated dis- counted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale" formu- lation of the dynamic programming principle.