Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations
Julien Michel, Didier Piau (2010)
ESAIM: Probability and Statistics
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We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every L norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these...