An approximation scheme for the optimal control of diffusion processes

We present a numerical approximation scheme for the infinite horizon problem related to diffusion processes. The scheme is based on a discrete version of the dynamic programming principle and converges to the viscosity solution of the second order Hamilton-Jacobi-Bellman equation. The diffusion can be degenerate. The problem R(n) is solved in a bounded domain Omega using a truncation technique and without imposing invariance conditions on Omega. We prove explicit estimates of the error due to the truncation technique.