Using systematically a tricky idea of N.V. Krylov, we obtain
general results on the rate of convergence of a certain class of
monotone approximation schemes for stationary
Hamilton-Jacobi-Bellman equations with variable coefficients.
This result applies in particular to control schemes based on the
dynamic programming principle and to finite difference schemes
despite, here, we are not able to treat the most general case.
General results have been obtained earlier by Krylov for
finite difference schemes in the stationary case with constant
coefficients and in the time-dependent case with variable
coefficients by using control theory and probabilistic methods.
In this paper we are able to handle variable coefficients by a
purely analytical method. In our opinion this way is far simpler
and, for the cases we can treat, it yields a better rate of
convergence than Krylov obtains in the variable coefficients case.