Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||385 - 411|
|Published online||17 August 2007|
Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
Université Ferhat Abbas, Fac. Sciences, Dépt. Maths., Sétif 19000, Algeria; firstname.lastname@example.org
2 CMI, LATP – CNRS and Université de Provence, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France; email@example.com
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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