Homogenization of a singular random one-dimensional PDE
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 3, p. 519-543

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.

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.

DOI : https://doi.org/10.1214/07-AIHP134
Classification:  74Q10
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {3},
     year = {2008},
     pages = {519-543},
     doi = {10.1214/07-AIHP134},
     zbl = {1172.74043},
     mrnumber = {2451056},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 44 (2008) no. 3, pp. 519-543. doi : 10.1214/07-AIHP134. http://www.numdam.org/item/AIHPB_2008__44_3_519_0/

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