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Large deviations, central limit theorems and $L^{p}$ convergence for Young measures and stochastic homogenizations

Julien Michel; Didier Piau — 1998

ESAIM: Probability and Statistics

Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations

Julien Michel; Didier Piau — 2010

ESAIM: Probability and Statistics

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 results...

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Large deviations, central limit theorems and L p convergence for Young measures and stochastic homogenizations

Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations

Large deviations, central limit theorems and $L^{p}$ convergence for Young measures and stochastic homogenizations