Error bounds for monotone approximation schemes for parabolic   Hamilton-Jacobi-Bellman equations
  We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general results to various schemes including finite difference schemes, splitting methods and the classical approximation by piecewise constant controls. 
Guy Barles (LMPT), Espen R. Jakobsen