A GENERIC APPROACH TO HOMOGENIZATION OF A DIFFUSION DRIVEN BY GROWING INCOMPRESSIBLE DRIFT

Brice Franke (1) , Shuenn-Jyi Sheu (2)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
2 NCU - National Central University [Taiwan]

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.

Mots clés: non-reversible diffusion; fast incompressible drift; Hunt process; distributional limit theorem

Domaines: Probabilités [math.PR]

Brice Franke, Shuenn-Jyi Sheu. A GENERIC APPROACH TO HOMOGENIZATION OF A DIFFUSION DRIVEN BY GROWING INCOMPRESSIBLE DRIFT. 2024. ⟨hal-04571702⟩