  This paper is devoted to establish continuous dependence estimates for the
ergodic problem for Bellman operators (namely, estimates of (v_1-v_2) where v_1
and v_2 solve two equations with different coefficients). We shall obtain an
estimate of ||v_1-v_2||_\infty with an explicit dependence on the
L^\infty-distance between the coefficients and an explicit characterization of
the constants and also, under some regularity conditions, an estimate of
||v_1-v_2||_{C^2(\R^n)}.
  Afterwards, the former result will be crucial in the estimate of the rate of
convergence for the homogenization of Bellman equations. In some regular cases,
we shall obtain the same rate of convergence established in the monographs
[11,26] for regular linear problems.
