EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Free access article

Issue ESAIM: PS
Volume 2, 1998
Page(s) 135 - 161
DOI 10.1051/ps:1998105

ESAIM: P&S, 1998, Vol. 2, pp. 135-161
DOI: 10.1051/ps:1998105

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

Julien Michel1 and Didier Piau2

1  (jmichel@umpa.ens-lyon.fr)
2  (piau@jonas.univ-lyon1.fr)


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.


Résumé
Nous étudions les processus d'homogénéisation stochastique considérés par Baldi (1988) et par Facchinetti and Russo (1983). Nous précisons la vitesse de convergence vers l'état homogénéisé en démontrant les résultats suivants : (i) les mesures de Young associées vérifient un principe de grandes déviations ; si on considère les valeurs prises par les mesures de Young en une fonction donnée, alors (ii) la vitesse de convergence de ces valeurs est bornée dans tous les Lp par un taux explicite et (iii) elles vérifient un théorème central limite. En dimension 1, nous appliquons ces résultats à l'homogénéisation stochastique de p-laplaciens aléatoires, pour tout p > 1.


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


© EDP Sciences, SMAI 1998


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.