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Quantitative version of the Kipnis–Varadhan theorem and Monte Carlo approximation of homogenized coefficients

2013
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The Annals of Applied Probability
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This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the point of view of the random walk in a random environment. Given some final time t>0, a natural approximation of the homogenized coefficients is given by the empirical average of the final squared positions re-scaled by t of n independent random

doi:10.1214/12-aap880
fatcat:d65kahlfpzbo3ce5mybth7kfh4