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

Michel, Julien, and Piau, Didier. "Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations." ESAIM: Probability and Statistics 2 (2010): 135-161. <http://eudml.org/doc/197752>.

@article{Michel2010,
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. },
author = {Michel, Julien, Piau, Didier},
journal = {ESAIM: Probability and Statistics},
keywords = {Stochastic homogenization / large deviations / Young measures / limit theorems / rate of convergence. ; stochastic homogenization; large deviations; Young measures},
language = {eng},
month = {3},
pages = {135-161},
publisher = {EDP Sciences},
title = {Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations},
url = {http://eudml.org/doc/197752},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Michel, Julien
AU - Piau, Didier
TI - Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 2
SP - 135
EP - 161
AB - 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.
LA - eng
KW - Stochastic homogenization / large deviations / Young measures / limit theorems / rate of convergence. ; stochastic homogenization; large deviations; Young measures
UR - http://eudml.org/doc/197752
ER -