A GENERIC APPROACH TO HOMOGENIZATION OF A DIFFUSION DRIVEN BY GROWING INCOMPRESSIBLE DRIFT - Université Bretagne Sud Access content directly
Preprints, Working Papers, ... Year : 2024

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

Shuenn-Jyi Sheu
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Abstract

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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hal-04571702 , version 1 (08-05-2024)

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