Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 4, p. 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 : https://doi.org/10.1214/08-AIHP190
Classification:  60F17
Keywords: homogenization, random medium, degenerate diffusion, locally stationary environment
@article{AIHPB_2009__45_4_981_0,
     author = {Rhodes, R\'emi},
     title = {Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {4},
     year = {2009},
     pages = {981-1001},
     doi = {10.1214/08-AIHP190},
     zbl = {1207.60029},
     mrnumber = {2572160},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2009__45_4_981_0}
}
Rhodes, Rémi. Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 4, pp. 981-1001. doi : 10.1214/08-AIHP190. http://www.numdam.org/item/AIHPB_2009__45_4_981_0/

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