A GENERIC APPROACH TO HOMOGENIZATION OF A DIFFUSION DRIVEN BY GROWING INCOMPRESSIBLE DRIFT
Résumé
We study how the resolvent-family of a diffusion behaves, as the
drift grows to infinity. The limit turns out to be a selfadjoint pseudo-resolvent.
After reduction of the underlying Hilbert-space, this pseudo-resolvent becomes
a resolvent to a strongly continuous semi-group of contractions. We prove that
this semi-group is associated to some Hunt-process on some suitable state-
space which is constructed from equivalence classes of the drifts trajectories.
Finally, we show a distributional limit theorem for the accelerated diffusion
toward the associated Hunt process.
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