Solution of the Stochastic Control Problem in Unbounded Domains

Bellman’s dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently dejhed in an unbounded domain. Ezi.sting methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, usin,q the fact that Poisson impulse noise tends to a Gausaian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive appvoxirnation and quasi-linearization and is inherently more efftcient than existing methods of solution.