Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 981-1001.

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.

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.

DOI : 10.1214/08-AIHP190
Classification : 60F17
Mots-clés : homogenization, random medium, degenerate diffusion, locally stationary environment 
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Rhodes, Rémi. Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 981-1001. doi : 10.1214/08-AIHP190. http://www.numdam.org/articles/10.1214/08-AIHP190/

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