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Homogenization of a semilinear parabolic PDE with locally periodiccoefficients: a probabilistic approach

Published online by Cambridge University Press:  17 August 2007

Abdellatif Benchérif-Madani  and
Étienne Pardoux
Abdellatif Benchérif-Madani
Affiliation:
Université Ferhat Abbas, Fac. Sciences, Dépt. Maths., Sétif 19000, Algeria; lotfi_madani@yahoo.fr
Étienne Pardoux
Affiliation:
CMI, LATP – CNRS and Université de Provence, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France; pardoux@latp.unimrs.fr
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Abstract

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.

Keywords

Homogenizationnonlinear parabolic PDEPoisson equationdiffusion approximationbackward SDE.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 385 - 411
Copyright
© EDP Sciences, SMAI, 2007

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