Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

Rémi Rhodes

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 981-1001
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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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 45.4 (2009): 981-1001. <http://eudml.org/doc/78064>.

@article{Rhodes2009,
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 [Probab. Theory Related Fields (2009)] and improves this latter work by considering possibly degenerate diffusion matrices.},
author = {Rhodes, Rémi},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {homogenization; random medium; degenerate diffusion; locally stationary environment; stochastic differential equation; locally stationary coefficients},
language = {eng},
number = {4},
pages = {981-1001},
publisher = {Gauthier-Villars},
title = {Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix},
url = {http://eudml.org/doc/78064},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Rhodes, Rémi
TI - Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 981
EP - 1001
AB - 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.
LA - eng
KW - homogenization; random medium; degenerate diffusion; locally stationary environment; stochastic differential equation; locally stationary coefficients
UR - http://eudml.org/doc/78064
ER -

References

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  12. [12] R. Rhodes. On homogenization of space time dependent random flows. Stochastic Process. Appl. 117 (2007) 1561–1585. Zbl1127.60027MR2353040
  13. [13] R. Rhodes. Diffusion in a locally stationary random environment. Probab. Theory Related Fields 143 (2009) 545–568. Zbl1163.60049MR2475672
  14. [14] D. Stroock. Diffusion semi-groups corresponding to uniformly elliptic divergence form operators. In Séminaires de Probabilités XXII 316–347. Lecture Notes in Math. 1321. Springer, Berlin, 1988. (Section B 35 (1999) 121–141.) Zbl0651.47031MR960535
  15. [15] L. Wu. Forward–Backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes. Ann. Inst. H. Poincaré Probab. Statist. 35 (1999) 121–141. Zbl0936.60037MR1678517

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