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

Published online by Cambridge University Press:  15 August 2002

Julien Michel  and
Didier Piau
Julien Michel
Affiliation:
(jmichel@umpa.ens-lyon.fr)
Didier Piau
Affiliation:
(piau@jonas.univ-lyon1.fr)
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Abstract

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 Lp norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these results to the stochastic homogenization of random p-Laplacian operators for any p > 1.

Keywords

Stochastic homogenization / large deviations / Young measures / limit theorems / rate of convergence.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 2 , 1998 , pp. 135 - 161
Copyright
© EDP Sciences, SMAI, 1998

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