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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 periodiccoefficients is homogenized. We substantially weaken previous assumptions onthe coefficients. In particular, we prove new ergodic theorems. We show thatin such a weak setting on the coefficients, the proper statement of thehomogenization property concerns viscosity solutions, though we need abounded 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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