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  • Adams, Robert A.; Fournier, John J. F. Sobolev spaces. Second edition. Pure and Applied Mathematics (Amsterdam), 140. Elsevier/Academic Press, Amsterdam, 2003. xiv+305 pp. ISBN: 0-12-044143-8 MR2424078
  • Bensoussan, Alain; Lions, Jacques-Louis; Papanicolaou, George. Asymptotic analysis for periodic structures. Studies in Mathematics and its Applications, 5. North-Holland Publishing Co., Amsterdam-New York, 1978. xxiv+700 pp. ISBN: 0-444-85172-0 MR0503330
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • Delarue, François. Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients. Ann. Probab. 32 (2004), no. 3B, 2305--2361. MR2078542
  • E, Weinan; Li, Xiantao; Vanden-Eijnden, Eric. Some recent progress in multiscale modeling. Multiscale modelling and simulation, 3--21, Lect. Notes Comput. Sci. Eng., 39, Springer, Berlin, 2004. MR2089950
  • Freĭdlin, M. I. The Dirichlet problem for an equation with periodic coefficients depending on a small parameter. (Russian) Teor. Verojatnost. i Primenen. 9 1964 133--139. MR0163062
  • M. Hairer, phAn introduction to stochastic pdes, Lecture Notes, 2009.
  • Hairer, Martin; Pardoux, Etienne. Homogenization of periodic linear degenerate PDEs. J. Funct. Anal. 255 (2008), no. 9, 2462--2487. MR2473263
  • Ichihara, Naoyuki. Homogenization problem for stochastic partial differential equations of Zakai type. Stoch. Stoch. Rep. 76 (2004), no. 3, 243--266. MR2072382
  • Papanicolaou, G. C.; Stroock, D.; Varadhan, S. R. S. Martingale approach to some limit theorems. Papers from the Duke Turbulence Conference (Duke Univ., Durham, N.C., 1976), Paper No. 6, ii+120 pp. Duke Univ. Math. Ser., Vol. III, Duke Univ., Durham, N.C., 1977. MR0461684
  • Pardoux, Étienne. Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach. J. Funct. Anal. 167 (1999), no. 2, 498--520. MR1716206
  • Pavliotis, G. A.; Stuart, A. M. Periodic homogenization for inertial particles. Phys. D 204 (2005), no. 3-4, 161--187. MR2148377
  • Pavliotis, Grigorios A.; Stuart, Andrew M. Multiscale methods. Averaging and homogenization. Texts in Applied Mathematics, 53. Springer, New York, 2008. xviii+307 pp. ISBN: 978-0-387-73828-4 MR2382139
  • Reed, Michael; Simon, Barry. Methods of modern mathematical physics. I. Functional analysis. Second edition. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. xv+400 pp. ISBN: 0-12-585050-6 MR0751959
  • D. Revuz and M. Yor, phContinuous martingales and Brownian motion, third ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1999. MR1725357 (2000h:60050)
  • Sow, A. B.; Rhodes, R.; Pardoux, É. Homogenization of periodic semilinear parabolic degenerate PDEs. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, 979--998. MR2526412
  • Temam, Roger; Miranville, Alain. Mathematical modeling in continuum mechanics. Second edition. Cambridge University Press, Cambridge, 2005. xii+342 pp. ISBN: 978-0-521-61723-9; 0-521-61723-5 MR2169020
  • Wang, Wei; Cao, Daomin; Duan, Jinqiao. Effective macroscopic dynamics of stochastic partial differential equations in perforated domains. SIAM J. Math. Anal. 38 (2006/07), no. 5, 1508--1527. MR2286017
  • Wang, Wei; Duan, Jinqiao. Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions. Comm. Math. Phys. 275 (2007), no. 1, 163--186. MR2335772

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