Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Homogenization of a singular random one-dimensional PDE

Bogdan Iftimie, Étienne Pardoux, and Andrey Piatnitski

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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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 3 (2008), 519-543.

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1211819423

Digital Object Identifier
doi:10.1214/07-AIHP134

Mathematical Reviews number (MathSciNet)
MR2451056

Zentralblatt MATH identifier
1172.74043

Subjects
Primary: 74Q10: Homogenization and oscillations in dynamical problems

Keywords
Stochastic homogenization Random operators

Citation

Iftimie, Bogdan; Pardoux, Étienne; Piatnitski, Andrey. Homogenization of a singular random one-dimensional PDE. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 3, 519--543. doi:10.1214/07-AIHP134. https://projecteuclid.org/euclid.aihp/1211819423


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