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

ESAIM: Probability and Statistics (2010)

- Volume: 2, page 135-161
- ISSN: 1292-8100

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topMichel, 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 -

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