Homogenization of periodic semilinear parabolic degenerate PDEs

 Access to full text

 Full (PDF)

1. [1] Bensoussan A., Lions J.L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, North-Holland, 1978. Zbl0404.35001MR503330
2. [2] Briand P., Hu Y., Stability of BSDEs with random terminal time and homogenization of semilinear elliptic PDEs, J. Funct. Anal.155 (1998) 455-494. Zbl0912.60081MR1624569
3. [3] Buckdahn R., Hu Y., Peng S., Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs, NoDEA Nonlinear Differential Equations Appl.6 (4) (1999) 395-411. Zbl0953.35017MR1736544
4. [4] Crandall M., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1992) 1-67. Zbl0755.35015MR1118699
5. [5] De Arcangelis R., Serra Cassano F., On the homogenization of degenerate elliptic equations in divergence form, J. Math. Pures Appl.71 (1992) 119-138. Zbl0678.35036MR1170248
6. [6] Delarue F., On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stochastic Process. Appl.99 (2) (2002) 209-286. Zbl1058.60042MR1901154
7. [7] Delarue F., Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients, Ann. Probab. B32 (3) (2004) 2305-2361. Zbl1073.35021MR2078542
8. [8] Delarue F., Rhodes R., Stochastic homogenization of quasilinear PDEs with a spatial degeneracy, Asymptot. Anal., in press, available on, http://hal.archives-ouvertes.fr/. Zbl1180.35591MR2499193
9. [9] Diop M.A., Iftimie B., Pardoux E., Piatnitski A., Singular homogenization with stationary in time and periodic in space coefficients, J. Funct. Anal.231 (2006) 1-46. Zbl1113.35015MR2190162
10. [10] Engström J., Persson L.-E., Piatnitski A., Wall P., Homogenization of random degenerated nonlinear monotone operators, Glas. Mat. Ser. III41 (61) (2006) 101-114. Zbl1118.35003MR2242396
11. [11] Ethier S.N., Kurtz T.G., Markov Processes, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1986. Zbl0592.60049MR838085
12. [12] Freidlin M., The Dirichlet problem for an equation with periodic coefficients depending on a small parameter, Teor. Veroyatnost. i Primenen.9 (1964) 133-139. Zbl0138.11602MR163062
13. [13] Hairer M., Pardoux E., Homogenization of periodic linear degenerate PDEs, available on, arXiv:math/0702304v1. Zbl1167.60015MR2473263
14. [14] Heron B., Mossino J., H-convergence and regular limits for stratified media with low and high conductivities, Appl. Anal.57 (3–4) (1995) 271-308. Zbl0833.35010MR1384376
15. [15] Huang Y., Su N., Zhang X., Homogenization of degenerate quasilinear parabolic equations with periodic structure, Asymptotic Anal.48 (2006) 77-89. Zbl1157.35313MR2233379
16. [16] Jakobsen E.R., Karlsen K.H., Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations, J. Differential Equations183 (2002) 497-525. Zbl1086.35061MR1919788
17. [17] A. Lejay, Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme divergence, Thèse de l'université de Provence, 2000. 
18. [18] Meyer P.A., Zheng W.A., Tightness criteria for laws of semartingales, Ann. Inst. Henri Poincaré20 (1984) 353-372. Zbl0551.60046MR771895
19. [19] Pardoux E., Homogenization of a linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach, J. Funct. Anal.167 (1999) 498-520. Zbl0935.35010MR1716206
20. [20] Pardoux E., BSDEs, weak convergence and homogenization of semilinear PDEs, in: Clarke F.H., Stern R.J. (Eds.), Nonlinear Analysis, Differential Equations and Control, Kluwer Acad. Publ., 1999, pp. 503-549. Zbl0959.60049MR1695013
21. [21] Pardoux E., Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, in: Decreusefond L., Gjerde J., Oksendal B., Üstünel A.S. (Eds.), Stochastic Analysis and Related Topics VI: The Geilo Workshop, 1996, Birkhäuser, 1998, pp. 79-127. Zbl0893.60036MR1652339
22. [22] Pardoux E., Peng S., Backward stochastic differential equations and quasilinear parabolic partial differential equations, in: Rozovskii B.L., Sowers R.S. (Eds.), Stochastic Partial Differential Equations and their Applications, Lecture Notes in Control & Information Sciences, vol. 176, Springer, Berlin, 1992, pp. 200-217. Zbl0766.60079MR1176785
23. [23] Pardoux E., Veretennikov A.Yu., Averaging of backward stochastic differential equations with application to semilinear PDE's, Stochastics Stochastic Rep.60 (1997) 255-270. Zbl0891.60053MR1467720
24. [24] Pardoux E., Veretennikov A.Yu., On Poisson equation and diffusion approximation 1, Ann. Probab.29 (2001) 1061-1085. Zbl1029.60053MR1872736
25. [25] Pardoux E., Yu Veretennikov A., On Poisson equation and diffusion approximation 3, Ann. Probab.33 (2005). Zbl1071.60022MR2135314
26. [26] Paronetto F., Serra Cassano F., On the convergence of a class of degenerate parabolic equations, J. Math. Pures Appl.77 (1998) 851-878. Zbl0920.35082MR1656776
27. [27] Paronetto F., Homogenization of a class of degenerate parabolic equations, Asymptotic Anal.21 (1999) 275-302. Zbl0945.35009MR1728026
28. [28] Paronetto F., Homogenization of degenerate elliptic-parabolic equations, Asymptotic Anal.37 (2004) 21-56. Zbl1052.35025MR2035361
29. [29] Rhodes R., On homogenization of space-time dependent and degenerate random flows, Stochastic Process. Appl.117 (2007) 1561-1585. Zbl1127.60027MR2353040
30. [30] R. Rhodes, Homogenization of locally ergodic diffusions with possibly degenerate diffusion matrix, Ann. Inst. H. Poincaré Probab. Statist., in press. Zbl1207.60029