EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 37, Issue 1, 2001, Pages 1-42

  Gaudron, Guillaume ^a   Pardoux, Etienne ^b  

^a CNRS   (France)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Convergence de processus; quations diff rentielles stochastiques r trogrades; EDP semi lin aires paraboliques; Homog n isation; Milieux al atoires; Milieux p riodiques; Random media; Syst mes

Indexed keywords

EID: 0346311466     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(00)01058-X     Document Type: Article

References (26)

1. Avellaneda M., Majda A. Mathematical models with exact renormalization for turbulent transport. Comm. Math. Phys. Vol. 131:1990;381-429.
2. Avellaneda M., Majda A. 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.
3. Bensoussan A., Boccardo L., Murat F. H convergence for quasi-linear elliptic equations with quadratic growth. Appl. Math. Optim. Vol. 26:1992;253-272.
4. Bensoussan A., Lions J.L., Papanicolaou G. Asymptotic Analysis for Periodic Structure. Stud. Math. Appl. Vol. 5:1978;North-Holland, Amsterdam.
5. Briand P., Hu Y. Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs. J. Funct. Anal. Vol. 155:(2):1998;455-494.
6. Buckdahn R., Hu Y. Probabilistic approach to homogenizations of systems of quasi-linear parabolic PDEs with periodic structure. Nonlinear Anal. Vol. 32:(5):1998;609-619.
7. Carmona R., Xu L. Homogenization for time-dependent two-dimensional incompressible Gaussian flows. Ann. Appl. Probab. Vol. 7:(1):1997;265-279.
8. Dermoune A., Hamadene S., Ouknine Y. Backward stochastic differential equation with local time. Stochastics. Vol. 66:1999;103-119.
9. Freidlin M. Markov processes and differential equations: asymptotic problems. Lectures in Mathematics. 1996;137-152 ETH Zürich, Birkhäuser, Basel. chapter 11.
10. Gaudron G. Scaling laws and convergence for the advection-diffusion equation. Ann. Appl. Probab. Vol. 8:(3):1998;649-663.
11. Gaudron G., On convergence of BSDE's and homogenization of elliptic semi-linear PDE's (soumis pour publication).
12. Jacod J., Shiryaev A.N. Limit Theorems for Stochastic Processes. Grundlehren Math. Wiss. Vol. 288:1987;Springer-Verlag, New York.
13. Kobylanski M. 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.
14. Kobylanski M., Backward stochastic differential equations and partial differential equations with quadratic growth (soumis pour publication).
15. Komorowski T., Papanicolaou G. Motion in a Gaussian, incompressible flow. Ann. Appl. Probab. Vol. 7:(1):1997;229-264.
16. Krylov N.V. Controlled Diffusion Processes. Appl. Math. Vol. 14:1980;Springer-Verlag, New York.
17. Landim C., Olla S., Yau H.T. Convection diffusion equation with space-time ergodic random flow. Probab. Theory Related Fields. Vol. 112:1998;203-220.
18. Meyer P.A., Zheng W.A. Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré, Probab. Statist. Vol. 20:1984;353-372.
19. Olla S. Homogenization of Diffusion Processes in Random Fields. Cours de l'École Doctorale de l'École Polytechnique. 1994.
20. Pardoux E. BSDE's and semilinear PDE's Stochastic Analysis and Related Topics VI, The Geilo Workshop 1996. Progress in Probability. Vol. 42:1998;79-127 Birkhauser, Basel.
21. Pardoux E. BSDE's, weak convergence and homogenization of semilinear PDE's. Clarke F.H., Stern R.J. Nonlinear Analysis, Differential Equations and Control. 1999;503-549 Kluwer, Dordrecht.
22. Pardoux E., Peng S. Adapted solution of a backward stochastic differential equation. Systems Control Lett. Vol. 14:1990;55-61.
23. Pardoux E., Peng S. Backward SDEs and quasilinear PDEs. Rozovskii B.L., Sowers R.B. Stochastic Partial Differential Equations and Their Applications, LNCIS 176. 1992;Springer, New York.
24. Pardoux E., Veretennikov A.Y. Averaging for backward stochastic differential equations, with application to semi-linear PDE's. Stochastics Stochastics Rep. Vol. 60:(3-4):1997;355-370.
25. Pardoux E., Veretennikov A.Y., On Poisson equation and diffusion approximation, Annals of Probability (à paraître).
26. Protter P. Stochastic Integration and Differential Equations, A New Approach. Appl. Math. 21. 1995;Springer, New York.