zbMATH — the first resource for mathematics

On homogenization of space-time dependent and degenerate random flows. (English) Zbl 1127.60027
The author considers a homogenization problem with ergodic control and degenerate diffusion matrix along certain directions: he proves an existence theorem and an invariance principle, and applies the theory to chessboard-like structures.

60F17 Functional limit theorems; invariance principles
60J60 Diffusion processes
Full Text: DOI
[1] Bhattacharya, R.N.; Gupta, V.K.; Walker, H., Asymptotics of solute dispersion in periodic media, SIAM J. appl. math., 49, 1, 86-98, (1989) · Zbl 0664.60079
[2] Fannjiang, C.; Komorowski, T., An invariance principle for diffusion in turbulence, Ann. probab., 27, 2, 751-781, (1999) · Zbl 0943.60030
[3] Fannjiang, C.; Komorowski, T., Diffusion approximation for particle convection in Markovian flows, Bull. Pol. acad. sci. math., 48, 3, 253-275, (2000) · Zbl 0959.60017
[4] Fannjiang, C.; Komorowski, T., Invariance principle for a diffusion in a Markov field, Bull. Pol. acad. sci. math., 49, 1, 45-65, (2001) · Zbl 0992.60039
[5] Fukushima, M.; Oshima, Y.; Takeda, M., ()
[6] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, in: Grundlehren der mathematischen Wissenschaft, vol. 288, Springer-Verlag · Zbl 1018.60002
[7] Kipnis, C.; Varadhan, S.R.S., Central limit theorem for additive functionals of reversible Markov processes and application to simple exclusion, Ann. probab., 28, 1, 277-302, (2000)
[8] Kozlov, S.M., The method of averaging and walks in inhomogeneous environments, Russian math. surveys, 40, 73-145, (1985) · Zbl 0615.60063
[9] Kusuoka, S.; Stroock, D.W., Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator, Ann. of math., 127, 165-189, (1988) · Zbl 0699.35025
[10] Landim, C.; Olla, S.; Yau, H.T., Convection – diffusion equation with space – time ergodic random flow, Probab. theory related fields, 112, 203-220, (1998) · Zbl 0914.60070
[11] Komorowski, T.; Olla, S., On homogenization of time-dependent random flows, Probab. theory related fields, 121, 98-116, (2001) · Zbl 0996.60040
[12] Ma, Z.M.; Röckner, M., Introduction to the theory of (non-symmetric) Dirichlet forms, (1992), Universitext, Springer-Verlag Berlin, Heidelberg
[13] Oelschläger, K., Homogenization of a diffusion process in a divergence free random field, Ann. probab., 16, 1084-1126, (1988) · Zbl 0653.60047
[14] S. Olla, Homogenization of diffusion processes in Random Fields, Cours de l’école doctorale, Ecole polytechnique, 1994
[15] Osada, H., (), 507-517
[16] Pardoux, E., Homogenization of periodic linear degenerate PDEs, LATP, (2005), Université de Provence Marseille
[17] E. Pardoux, Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach, J. Funct. Anal., 167, 498-520 · Zbl 0935.35010
[18] Protter, P., ()
[19] Rudin, W., Analyse fonctionnelle, (1995), Ediscience International
[20] Sethuraman, S.; Varadhan, S.R.S.; Yau, H.T., Diffusive limit of a tagged particle in asymmetric simple exclusion processes, Commun. pure appl. math., 53, 972-1006, (2000) · Zbl 1029.60084
[21] Sznitman, A.S.; Zeitouni, O., An invariance principle for isotropic diffusions in random environment, C. R. acad. sci. Paris, ser. I, 339, 429-434, (2004) · Zbl 1051.60097
[22] Wu, L., Forward – backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes, Ann. inst. H. Poincaré, 35, 121-141, (1999) · Zbl 0936.60037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.