Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

Rémi Rhodes

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 4 (2009), 981-1001.

First available in Project Euclid: 6 November 2009

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Primary: 60F17: Functional limit theorems; invariance principles

homogenization random medium degenerate diffusion locally stationary environment


Rhodes, Rémi. Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 4, 981--1001. doi:10.1214/08-AIHP190.

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