Perturbed Stochastic Linear Regulator Problems

This paper is concerned with the approximate solution of stochastic optimal control problems which arise by perturbing the stochastic linear regulator problem, through an additive term with a small parameter $\delta $ in the drift coefficient of the unperturbed dynamical equations. The system states are assumed completely observable. Our main results concern expansions of solutions of the perturbed equation in powers $\delta ,\delta ^2 ,\delta ^3 , \cdots $ of the small parameter $\delta $.