Grossissement d'une filtration et retournement du temps d'une diffusion
EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
Homogenization of periodic semilinear hypoelliptic PDEs
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.
Probabilistic interpretation of a system of semi-linear parabolic partial differential equations
Homogenization of a singular random one-dimensional PDE
This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.
Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
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.
Stratonovich stochastic differential equations driven by general semimartingales
Homogenization of semilinear PDEs with discontinuous averaged coefficients.
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