Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations

Abstract. We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for par-abolic Hamilton-Jacobi-Bellman Equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank-Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant con-trols. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here. 1