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arXiv · 2211.13279

Green function and invariant measure estimates for nondivergence form elliptic homogenization

Scott Armstrong·Benjamin Fehrman·Jessica Lin
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Abstract

We prove quantitative estimates on the the parabolic Green function and the stationary invariant measure in the context of stochasic homogenization of elliptic equations in nondivergence form. We consequently obtain a quenched, local CLT for the corresponding diffusion process and a quantitative ergodicity estimate for the environmental process. Each of these results are characterized by deterministic (in terms of the environment) estimates which are valid above a random, ``minimal'' length scale, the stochastic moments of which we estimate sharply.

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Scott Armstrong, Benjamin Fehrman, Jessica Lin. 2022-11-23. Green function and invariant measure estimates for nondivergence form elliptic homogenization. https://arxiv.org/abs/2211.13279

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