Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
Rémi Rhodes
Source: Ann. Inst. H. Poincaré Probab. Statist. Volume 45, Number 4
(2009), 981-1001.
Abstract
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by considering possibly degenerate diffusion matrices.
Résumé
Nous étudions l’homogénéisation d’opérateurs paraboliques du second ordre sous forme divergence à coefficients localement stationnaires. Ces coefficients présentent deux échelles d’évolution: une évolution microscopique presque constante et une évolution macroscopique régulière. La théorie de l’homogénéisation consiste à donner une approximation macroscopique de l’opérateur initial qui tient compte des hétérogénéités microscopiques. Cet article fait suite à [Probab. Theory Related Fields (2009)] et généralise ce dernier en considérant des matrices de diffusion pouvant dégénérer.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aihp/1257529888
Digital Object Identifier: doi:10.1214/08-AIHP190
Zentralblatt MATH identifier: 05758866
Mathematical Reviews number (MathSciNet): MR2572160
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