# Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

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

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

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topRhodes, 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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- [13] R. Rhodes. Diffusion in a locally stationary random environment. Probab. Theory Related Fields 143 (2009) 545–568. Zbl1163.60049MR2475672
- [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
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