Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

From averaging to homogenization in cellular flows – An exact description of the transition

Martin Hairer, Leonid Koralov, and Zsolt Pajor-Gyulai

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Abstract

We consider a two-parameter averaging-homogenization type elliptic problem together with the stochastic representation of the solution. A limit theorem is derived for the corresponding diffusion process and a precise description of the two-parameter limit behavior for the solution of the PDE is obtained.

Résumé

Nous considérons un problème elliptique de type moyennisation / homogénisation à deux paramètres, en combinaison avec la représentation stochastique de la solution. Nous obtenons un théorème limite pour le processus de diffusion correspondant ainsi qu’une description précise du comportement limite de la solution de l’EDP.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 4 (2016), 1592-1613.

Dates
Received: 4 July 2014
Revised: 20 April 2015
Accepted: 26 May 2015
First available in Project Euclid: 17 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1479373241

Digital Object Identifier
doi:10.1214/15-AIHP690

Mathematical Reviews number (MathSciNet)
MR3573288

Zentralblatt MATH identifier
1356.35033

Subjects
Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]

Keywords
Local time Diffusion on graphs Averaging Homogenization

Citation

Hairer, Martin; Koralov, Leonid; Pajor-Gyulai, Zsolt. From averaging to homogenization in cellular flows – An exact description of the transition. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 4, 1592--1613. doi:10.1214/15-AIHP690. https://projecteuclid.org/euclid.aihp/1479373241


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