EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 1, pp. 1-42.
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Gaudron, Guillaume; Pardoux, Etienne. EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 1, pp. 1-42. http://www.numdam.org/item/AIHPB_2001__37_1_1_0/

1 M. Avellaneda, A. Majda, Mathematical models with exact renormalization for turbulent transport, Comm. Math. Phys. Vol. 131 (1990) 381-429. | MR | Zbl

2 M. Avellaneda, A. Majda, An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows, Comm. Math. Phys. Vol. 138 (1991) 339-391. | MR | Zbl

3 A. Bensoussan, L. Boccardo, F. Murat, H convergence for quasi-linear elliptic equations with quadratic growth, Appl. Math. Optim. Vol. 26 (1992) 253-272. | MR | Zbl

4 A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Stud. Math. Appl., Vol. 5, North-Holland, Amsterdam, 1978. | MR | Zbl

5 P. Briand, Y. Hu, Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, J. Funct. Anal. Vol. 155 (2) (1998) 455-494. | MR | Zbl

6 R. Buckdahn, Y. Hu, Probabilistic approach to homogenizations of systems of quasi-linear parabolic PDEs with periodic structure, Nonlinear Anal. Vol. 32 (5) (1998) 609-619. | MR | Zbl

7 R. Carmona, L. Xu, Homogenization for time-dependent two-dimensional incompressible Gaussian flows, Ann. Appl. Probab. Vol. 7 (1) (1997) 265-279. | MR | Zbl

8 A. Dermoune, S. Hamadene, Y. Ouknine, Backward stochastic differential equation with local time, Stochastics Vol. 66 (1999) 103-119. | MR | Zbl

9 M. Freidlin, Markov processes and differential equations: asymptotic problems, in: Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1996, pp. 137-152, chapter 11. | MR | Zbl

10 G. Gaudron, Scaling laws and convergence for the advection-diffusion equation, Ann. Appl. Probab. Vol. 8 (3) (1998) 649-663. | MR | Zbl

11 Gaudron G., On convergence of BSDE's and homogenization of elliptic semi-linear PDE's (soumis pour publication). | Zbl

12 J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Grundlehren Math. Wiss., Vol. 288, Springer-Verlag, New York, 1987. | MR | Zbl

13 M. Kobylanski, Résultat d'existence et d'unicité pour des EDSR avec des générateurs à croissance quadratique, Notes aux CRAS, Sér I Vol. 324 (1997) 81-86. | Zbl

14 Kobylanski M., Backward stochastic differential equations and partial differential equations with quadratic growth (soumis pour publication). | Zbl

15 T. Komorowski, G. Papanicolaou, Motion in a Gaussian, incompressible flow, Ann. Appl. Probab. Vol. 7 (1) (1997) 229-264. | MR | Zbl

16 N.V. Krylov, Controlled Diffusion Processes, Appl. Math., Vol. 14, Springer-Verlag, New York, 1980. | MR | Zbl

17 C. Landim, S. Olla, H.T. Yau, Convection diffusion equation with space-time ergodic random flow, Probab. Theory Related Fields Vol. 112 (1998) 203-220. | MR | Zbl

18 P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales, Ann. Inst. H. Poincaré, Probab. Statist. Vol. 20 (1984) 353-372. | Numdam | MR | Zbl

19 S. Olla, Homogenization of Diffusion Processes in Random Fields, Cours de l'École Doctorale de l'École Polytechnique, 1994.

20 E. Pardoux, BSDE's and semilinear PDE's Stochastic Analysis and Related Topics VI, The Geilo Workshop 1996, in: Progress in Probability, Vol. 42, Birkhauser, Basel, 1998, pp. 79-127. | MR | Zbl

21 E. Pardoux, BSDE's, weak convergence and homogenization of semilinear PDE's, in: Clarke F.H., Stern R.J. (Eds.), Nonlinear Analysis, Differential Equations and Control, Kluwer, Dordrecht, 1999, pp. 503-549. | MR | Zbl

22 E. Pardoux, S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. Vol. 14 (1990) 55-61. | MR | Zbl

23 E. Pardoux, S. Peng, Backward SDEs and quasilinear PDEs, in: Rozovskii B.L., Sowers R.B. (Eds.), Stochastic Partial Differential Equations and Their Applications, LNCIS 176, Springer, New York, 1992. | MR | Zbl

24 E. Pardoux, A.Y. Veretennikov, Averaging for backward stochastic differential equations, with application to semi-linear PDE's, Stochastics Stochastics Rep. Vol. 60 (3-4) (1997) 355-370. | MR | Zbl

25 Pardoux E., Veretennikov A.Y., On Poisson equation and diffusion approximation, Annals of Probability (à paraître). | Zbl

26 P. Protter, Stochastic Integration and Differential Equations, A New Approach, Appl. Math. 21, Springer, New York, 1995. | MR | Zbl