Near-optimal controls: stochastic case

Abstract

Near-optimization is as sensible and important as optimization for both theory and applications. In this paper, systems governed by the Ito stochastic differential equations are considered where both the drift and diffusion terms are allowed to depend on controls and the systems are allowed to be degenerate. Necessary and sufficient conditions for a control to be near-optimal are studied. Error estimates for the near-optimality are obtained based on some delicate estimates of the adjoint processes.