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Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

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Date
2009
Link to item file
http://hal.archives-ouvertes.fr/hal-00359976/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
degenerate coefficients; homogenization; random medium; locally stationary coefficients; diffusion process
Journal issue
Annales de l'I.H.P. Probabilités et Statistiques
Volume
45
Number
4
Publication date
2009
Article pages
981-1001
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/08-AIHP190
URI
https://basepub.dauphine.fr/handle/123456789/3127
Collections
  • CEREMADE : Publications
Metadata
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Author
Rhodes, Rémi
Type
Article accepté pour publication ou publié
Abstract (EN)
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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