Diffusion Approximation and Optimal Stochastic Control

In the paper a stochastic control model is studied, that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control, that satisfies a Lipschitz condition and is δ−optimal for the limit model, remains δ−optimal also in the prelimit model. The method of proof uses the technique of weak convergence of stochastic processes. The result that is obtained extends a previous work by the authors, where the limit model is deterministic.