Homogenization of periodic semilinear hypoelliptic PDEs
نویسندگان
چکیده
منابع مشابه
Homogenization of periodic semilinear parabolic degenerate PDEs
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 Rd . Our fully probabilistic method is based on the deep connection between PDEs and BSDEs and the weak convergence of a class of diffusion processe...
متن کامل[hal-00359844, v1] Homogenization of periodic semilinear parabolic degenerate PDEs
(a) LERSTAD, UFR S.A.T, Université Gaston Berger, BP 234, Saint-Louis, SENEGAL. email : [email protected] (b) CEREMADE, Université Paris-Dauphine, Place du maréchal De Lattre de Tassigny, 75775 Paris cedex 16, FRANCE. email : [email protected] (c) CMI, LATP-UMR 6632, Université de Provence, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, FRANCE. email : [email protected] Abstr...
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Abstract We study the long time behavior of an Ornstein–Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation. We also derive upper bounds on the convergence rate in several ...
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It is well-known under the name of ‘periodic homogenization’ that, under a centering condition of the drift, a periodic diffusion process on R converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of this result all rely on uniform ellipticity or hypoellipticity assumptions on the diffusion. In this paper, we considerably weaken these assumptions in order to ...
متن کاملHomogenization of a Periodic Degenerate Semilinear Elliptic Pde
In this paper a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novetly of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of Rd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2007
ISSN: 0240-2963
DOI: 10.5802/afst.1148