Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

2009/02/10 by Rémi Rhodes, Rhodes, Rémi
Mathematics · #28D05 (Secondary) #35K65 #60F17 (Primary) 35B27 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:28D05 #msc:35B27 #msc:35K65 #msc:60F17

paper · pdf · doi:10.48550/arxiv.0902.1586

To appear in Annales de l'institut henri poincare (link of the journal: http://www.imstat.org/aihp/)

arxiv created 2009/02/10 · arxiv updated 2009/12/01

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 "Diffusion in a locally stationary random environment" (published in Probability Theory and Related Fields) and improves this latter work by considering possibly degenerate diffusion matrices. The geometry of the homogenized equation shows that the particle is trapped in subspace of R^d.

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