| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 385 - 411 | |
| DOI | https://doi.org/10.1051/ps:2007026 | |
| Published online | 17 August 2007 | |
Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
1
Université Ferhat Abbas, Fac. Sciences, Dépt. Maths., Sétif 19000, Algeria; lotfi_madani@yahoo.fr
2
CMI, LATP – CNRS and Université de Provence,
39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France; pardoux@latp.unimrs.fr
Received:
28
March
2006
Revised:
6
December
2006
In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.
Mathematics Subject Classification: 35B27 / 60H30 / 60J60 / 60J35
Key words: Homogenization / nonlinear parabolic PDE / Poisson equation / diffusion approximation / backward SDE.
© EDP Sciences, SMAI, 2007
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