Displaying similar documents to “Homogenization of periodic semilinear parabolic degenerate PDEs”

Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach

Abdellatif Benchérif-Madani, Étienne Pardoux (2007)

ESAIM: Probability and Statistics

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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.

A Donsker theorem to simulate one-dimensional processes with measurable coefficients

Pierre Étoré, Antoine Lejay (2007)

ESAIM: Probability and Statistics

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In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.

Homogenization of periodic semilinear hypoelliptic PDEs

Alassane Diédhiou, Étienne Pardoux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.