no. 4
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

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.

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.

DOI : 10.1214/08-AIHP190
Classification : 60F17
Keywords: homogenization, random medium, degenerate diffusion, locally stationary environment 
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     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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     year = {2009},
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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

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