Homogenization of random semilinear PDEs

Probability Theory and Related Fields

Volumn 121, Issue 4, 2001, Pages 492-524

  Castell, Fabienne ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Homogenization; Random media

Indexed keywords

EID: 0035731258     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400100164     Document Type: Article

References (26)

1. Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic analysis for periodic structures. North Holland, (1978)
2. Briand, P., Hu, Y.: Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, Journal of Functional Analysis., 155(2), 455-494 (1998)
3. Bally, V., Pardoux, E., Stoica, L.: Backward stochastic differential equations associated to a symmetric Markov process. Submitted
4. Buckdahn, R., Hu, Y., Peng, S.: Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs, Nonlinear Differential Equations Appl., 6(4), 395-411 (1999)
5. De Masi, A., Ferrari, P.A., Golstein, S., Wick, W.D.: An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Statist. Phys., 55(3-4), 787-855 (1989)
6. Freidlin, M.: The Dirichlet Problem for an equation with periodic coefficients depending on a small parameter, Teor. Veoj. i Primenen., 9, 133-139 (1964)
7. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes, de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994
8. Gaudron, G., Pardoux, E.: EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires, Ann. Inst. H. Poincaré Probab. Statist 37(1), 1-42 (2001)
9. Hu, Y.: Stability theorems and homogenization of nonlinear PDEs with periodic structures. Pitman Research Notes in Mathematics, Longman 193-205 (1997)
10. Hu, Y., Peng, S.: A stability theorem of backward stochastic differential equations and its applications, C. R. Acad. Sci. Paris Sér. I Math., 324(9), 1059-1064 (1997)
11. Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Fnnctionals, Springer Verlag, (1994)
12. Kipnis, C., Varadhan, S.R.S: Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys., 104(1), 1-19 (1986)
13. Ladyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and quasilinear equations of parabolic type. Translations of Mathematical Monographs, Vol 23 American Mathematical Society, Providence, R.I, (1967)
14. Ladyzhenskaya, O.A. Ural'tseva N.N.: Linear and quasilinear elliptic equations, Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis Academic Press, New York-London, (1968)
15. Landim, C., Olla, S., Yau, H.T.: Convection-diffusion equation with space-time ergodic random flow, Probab. Theory Related Fields., 112(2), 203-220 (1998)
16. Lejay, A.: Méthodes probabilistic pour l'homogénéisation des opérateurs sous forme divergence: cas linéaire et semi-linéaire, Thèse de l'Université Aix-Marseille I, 2000
17. p-estimate for the gradient of solutions of second order elliptic divergence equations, Annali della Scuola. Norm. Sup. di Pisa 17, 189-206 (1963)
18. Olla, S.: Homogenization of diffusion processes in random fields. Cours de l'Ecole Doctorale de l'Ecole Polytechnique (1994)
19. Osada, H.: An invariance principle for Markov processes and Brownian particles with singular interaction, Ann. Inst. H. Poincaré Probab. Statist., 34(2), 217-248 (1998)
20. Osada, H., Saitoh, T.: An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains, Probab. Theory Related Fields., 101(1). 45-63 (1995)
21. Papanicolaou, G., Varadhan, S.R.S.: Boundary value problems with rapidly oscillating random coefficients., Colloquia Mathematica Societatis János Bolay, 27, Random Fields, Esztergom (Hungary) pp 835-873 (1979)
22. Pardoux, E.: BSDEs, weak convergence and homogenization of semilinear PDEs. Non linear analysis, differential equations and control (Montreal, QC, 1998) 503-549, NATO Sci. Ser. C Math. Phys. Sci., 528, Kluwer, (1999)
23. Pardoux, E.:Homogenization of linear and semilinear second order PDEs with periodic coefficients: a probabilistic approach. Journal of Functional Analysis., 167(2), 498-520 (1999)
24. Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14, 55-61 (1990)
25. Zeidler, E.: Nonlinear functional analysis and its applications II/B. Nonlinear monotone operators. Springer Verlag. New York-Berlin, (1990)
26. Zhikov, V.V.: On homogenization in random perforated domains of general t\pe, Matem. Zametki., 53(1), 41-58 (1993)