A central limit theorem for fluctuations in one dimensional stochastic homogenization

Yu Gu

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arXiv · 1508.05132

A central limit theorem for fluctuations in one dimensional stochastic homogenization

Yu Gu

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Abstract

In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with additive spatial white noise. Using a probabilistic approach, we obtain a precise error decomposition up to the first order, which helps to decompose the limiting Gaussian process, with one of the components corresponding to the corrector obtained by a formal two scale expansion.

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Yu Gu. 2015-08-20. A central limit theorem for fluctuations in one dimensional stochastic homogenization. https://arxiv.org/abs/1508.05132

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