  We study the quantitative homogenization of linear second order elliptic
equations in non-divergence form with highly oscillating periodic diffusion
coefficients and with large drifts, in the so-called ``centered'' setting where
homogenization occurs and the large drifts contribute to the effective
diffusivity. Using the centering condition and the invariant measures
associated to the underlying diffusion process, we transform the equation into
divergence form with modified diffusion coefficients but without drift. The
latter is in the standard setting for which quantitative homogenization results
have been developed systematically. An application of those results then yields
quantitative estimates, such as the convergence rates and uniform Lipschitz
regularity, for equations in non-divergence form with large drifts.
