Stochastic homogenization with space-time ergodic divergence-free drift
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Publication:6118760
DOI10.1214/23-AOP1663arXiv2207.14555OpenAlexW4391363465WikidataQ129004870 ScholiaQ129004870MaRDI QIDQ6118760
Author name not available (Why is that?)
Publication date: 28 February 2024
Published in: (Search for Journal in Brave)
Abstract: We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skew-symmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time-dependent, spatially-homogenous transport which, for mildly decorrelating fields, converges to a Brownian noise with deterministic covariance in the homogenization limit. The results apply to uniformly elliptic, stationary and ergodic environments in which the drift admits a suitably defined stationary and -integrable stream matrix.
Full work available at URL: https://arxiv.org/abs/2207.14555
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