Homogenization of a singular random one-dimensional PDE

Bogdan Iftimie; Étienne Pardoux; Andrey Piatnitski

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 3, page 519-543
  • ISSN: 0246-0203

Abstract

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This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.

How to cite

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Iftimie, Bogdan, Pardoux, Étienne, and Piatnitski, Andrey. "Homogenization of a singular random one-dimensional PDE." Annales de l'I.H.P. Probabilités et statistiques 44.3 (2008): 519-543. <http://eudml.org/doc/77981>.

@article{Iftimie2008,
abstract = {This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.},
author = {Iftimie, Bogdan, Pardoux, Étienne, Piatnitski, Andrey},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stochastic homogenization; random operators; random limit dynamics; convergence; random mixing coefficients},
language = {eng},
number = {3},
pages = {519-543},
publisher = {Gauthier-Villars},
title = {Homogenization of a singular random one-dimensional PDE},
url = {http://eudml.org/doc/77981},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Iftimie, Bogdan
AU - Pardoux, Étienne
AU - Piatnitski, Andrey
TI - Homogenization of a singular random one-dimensional PDE
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 3
SP - 519
EP - 543
AB - This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.
LA - eng
KW - stochastic homogenization; random operators; random limit dynamics; convergence; random mixing coefficients
UR - http://eudml.org/doc/77981
ER -

References

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