Error bounds for monotone schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

We provide the rate of convergence of general monotone numerical schemes for parabolic Hamilton-Jacobi-Bellman equations in bounded domains with Dirichlet boundary conditions. The so-called "shaking coefficients" technique introduced by Krylov is used. This technique is based on a perturbation of the dynamics followed by a regularization step by convolution. When restricting the equation to a domain, the perturbed problem may not satisfy such a restriction, so that a special treatment near the boundary is necessary.