Cet article traite de l'homogénéisation d'une équation aux dérivées partielles en dimension un d'espace, avec des coefficients aléatoires stationnaires et mélangeants, en présence d'u terme d'ordre zéro fortement oscillant. Nous montrons qu'avec un choix convenable du facteur d'échelle de ce terme d'ordre zéro, les solutions du problème étudié convergent en loi, et nous décrivons le processus limite. On peut noter que la dynamique limite est elle aussi aléatoire.
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.
Mots clés : stochastic homogenization, random operators
@article{AIHPB_2008__44_3_519_0, author = {Iftimie, Bogdan and Pardoux, \'Etienne and Piatnitski, Andrey}, title = {Homogenization of a singular random one-dimensional {PDE}}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {519--543}, publisher = {Gauthier-Villars}, volume = {44}, number = {3}, year = {2008}, doi = {10.1214/07-AIHP134}, mrnumber = {2451056}, zbl = {1172.74043}, language = {en}, url = {http://www.numdam.org/articles/10.1214/07-AIHP134/} }
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 SP - 519 EP - 543 VL - 44 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/07-AIHP134/ DO - 10.1214/07-AIHP134 LA - en ID - AIHPB_2008__44_3_519_0 ER -
%0 Journal Article %A Iftimie, Bogdan %A Pardoux, Étienne %A Piatnitski, Andrey %T Homogenization of a singular random one-dimensional PDE %J Annales de l'I.H.P. Probabilités et statistiques %D 2008 %P 519-543 %V 44 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/07-AIHP134/ %R 10.1214/07-AIHP134 %G en %F AIHPB_2008__44_3_519_0
Iftimie, Bogdan; Pardoux, Étienne; Piatnitski, Andrey. Homogenization of a singular random one-dimensional PDE. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 3, pp. 519-543. doi : 10.1214/07-AIHP134. http://www.numdam.org/articles/10.1214/07-AIHP134/
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