DISCRETE-TIME HIGH-ORDER SCHEMES FOR VISCOSITY SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS

A general method for constructing high-order approximation schemes for Hamilton-Jacobi-Bellman equations is given. The method is based on a discrete version of the Dynamic Programming Principle. We prove a general convergence result for this class of approximation schemes also obtaining, under more restrictive assumptions, an estimate in L(infinity) of the order of convergence and of the local truncation error. The schemes can be applied, in particular, to the stationary linear first order equation in R(n). We present several examples of schemes belonging to this class and with fast convergence to the solution.