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

Guillaume Gaudron; Etienne Pardoux

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 1, page 1-42
  • ISSN: 0246-0203

How to cite

top

Gaudron, Guillaume, and Pardoux, Etienne. "EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires." Annales de l'I.H.P. Probabilités et statistiques 37.1 (2001): 1-42. <http://eudml.org/doc/77682>.

@article{Gaudron2001,
author = {Gaudron, Guillaume, Pardoux, Etienne},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random media; periodic media; homogenization; convergence of stochastic processes; parabolic semilinear partial differential equations; backward stochastic differential equations},
language = {fre},
number = {1},
pages = {1-42},
publisher = {Elsevier},
title = {EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires},
url = {http://eudml.org/doc/77682},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Gaudron, Guillaume
AU - Pardoux, Etienne
TI - EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 1
SP - 1
EP - 42
LA - fre
KW - random media; periodic media; homogenization; convergence of stochastic processes; parabolic semilinear partial differential equations; backward stochastic differential equations
UR - http://eudml.org/doc/77682
ER -

References

top
  1. 1 M. Avellaneda, A. Majda, Mathematical models with exact renormalization for turbulent transport, Comm. Math. Phys.Vol. 131 (1990) 381-429. Zbl0703.76042MR1065678
  2. 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. Zbl0731.76082MR1108049
  3. 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. Zbl0795.35008MR1175481
  4. 4 A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis for Periodic Structure, Stud. Math. Appl., Vol. 5, North-Holland, Amsterdam, 1978. Zbl0404.35001MR503330
  5. 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. Zbl0912.60081MR1624569
  6. 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. Zbl1016.35002MR1612034
  7. 7 R. Carmona, L. Xu, Homogenization for time-dependent two-dimensional incompressible Gaussian flows, Ann. Appl. Probab.Vol. 7 (1) (1997) 265-279. Zbl0879.60063MR1428759
  8. 8 A. Dermoune, S. Hamadene, Y. Ouknine, Backward stochastic differential equation with local time, StochasticsVol. 66 (1999) 103-119. Zbl0930.60044MR1687807
  9. 9 M. Freidlin, Markov processes and differential equations: asymptotic problems, in: Lectures in Mathematics, ETH Zürich, Birkhäuser, Basel, 1996, pp. 137-152, chapter 11. Zbl0863.60049MR1399081
  10. 10 G. Gaudron, Scaling laws and convergence for the advection–diffusion equation, Ann. Appl. Probab.Vol. 8 (3) (1998) 649-663. Zbl0934.35215MR1627752
  11. 11 Gaudron G., On convergence of BSDE's and homogenization of elliptic semi-linear PDE's (soumis pour publication). Zbl1017.60077
  12. 12 J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Grundlehren Math. Wiss., Vol. 288, Springer-Verlag, New York, 1987. Zbl0635.60021MR959133
  13. 13 M. Kobylanski, Résultat d'existence et d'unicité pour des EDSR avec des générateurs à croissance quadratique, Notes aux CRAS, Sér IVol. 324 (1997) 81-86. Zbl0880.60061
  14. 14 Kobylanski M., Backward stochastic differential equations and partial differential equations with quadratic growth (soumis pour publication). Zbl1044.60045
  15. 15 T. Komorowski, G. Papanicolaou, Motion in a Gaussian, incompressible flow, Ann. Appl. Probab.Vol. 7 (1) (1997) 229-264. Zbl0880.60063MR1428758
  16. 16 N.V. Krylov, Controlled Diffusion Processes, Appl. Math., Vol. 14, Springer-Verlag, New York, 1980. Zbl0459.93002MR601776
  17. 17 C. Landim, S. Olla, H.T. Yau, Convection diffusion equation with space-time ergodic random flow, Probab. Theory Related FieldsVol. 112 (1998) 203-220. Zbl0914.60070MR1653837
  18. 18 P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales, Ann. Inst. H. Poincaré, Probab. Statist.Vol. 20 (1984) 353-372. Zbl0551.60046MR771895
  19. 19 S. Olla, Homogenization of Diffusion Processes in Random Fields, Cours de l'École Doctorale de l'École Polytechnique, 1994. 
  20. 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. Zbl0893.60036MR1652339
  21. 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. Zbl0959.60049MR1695013
  22. 22 E. Pardoux, S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett.Vol. 14 (1990) 55-61. Zbl0692.93064MR1037747
  23. 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. Zbl0766.60079MR1176785
  24. 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. Zbl0891.60053MR1467720
  25. 25 Pardoux E., Veretennikov A.Y., On Poisson equation and diffusion approximation, Annals of Probability (à paraître). Zbl1054.60064
  26. 26 P. Protter, Stochastic Integration and Differential Equations, A New Approach, Appl. Math. 21, Springer, New York, 1995. Zbl0694.60047MR1037262

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.