Homogenization of periodic semilinear  parabolic  degenerate PDEs

Pardoux, Etienne; Rhodes, Rémi; Sow, Bamba A.

Pardoux, Etienne; Rhodes, Rémi; Sow, Bamba A. (2009), Homogenization of periodic semilinear parabolic degenerate PDEs, Annales de l'Institut Henri Poincaré. Analyse non linéaire, 26, 3, p. 979-998. http://dx.doi.org/10.1016/j.anihpc.2008.09.001

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00359844/en/

Date

2009

Journal name

Annales de l'Institut Henri Poincaré. Analyse non linéaire

Volume

Number

Publisher

Elsevier

Pages

979-998

Abstract (EN)

In this paper a second order semilinear parabolic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some part of the space. Our fully probabilistic method is based on the deep connection between PDEs and BSDEs and the weak convergence of a class of diffusion processes.

Subjects / Keywords

hormander's theorem; periodic coefficients; backward stochastic differential equation; degenerate diffusion coefficient; homogenization