Approximations, Existence, and Numerical Procedures for Optimal Stochastic Controls

摘要

In the paper, the authors prove several convergence results for a numerical method in optimal stochastic control, based on finite difference approximations to the non-linear Bellman partial differential equation for the optimal cost. As a very useful by-product to the main development, the authors obtain new existence results for optimal controls, and interesting results on the approximation of a controlled diffusion by a controlled Markov chain. The methods and results are new, and depend on results concerning weak convergence of probability measures. The methods seem to be quite powerful, and have applications to many other problems in approximation and control. (Author)