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References

  1. Blömker, Dirk. Approximation of the stochastic Rayleigh-Bénard problem near the onset of convection and related problems. Stoch. Dyn. 5 (2005), no. 3, 441--474. MR2167309 (2006i:76086)
  2. Blömker, Dirk. Amplitude equations for stochastic partial differential equations. Interdisciplinary Mathematical Sciences, 3. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. x+126 pp. ISBN: 978-981-270-637-9; 981-270-637-2 MR2352975 (2009c:60165)
  3. Blömker, Dirk; Hairer, Martin. Multiscale expansion of invariant measures for SPDEs. Comm. Math. Phys. 251 (2004), no. 3, 515--555. MR2102329 (2005m:60130)
  4. Blömker, Dirk; Hairer, Martin. Amplitude equations for SPDEs: approximate centre manifolds and invariant measures. Probability and partial differential equations in modern applied mathematics, 41--59, IMA Vol. Math. Appl., 140, Springer, New York, 2005. MR2202032

  5. Blömker, D.; Hairer, M.; Pavliotis, G. A. Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities. Nonlinearity 20 (2007), no. 7, 1721--1744. MR2335080 (2008e:60186)

  6. Chekhlov, Alexei; Yakhot, Victor. Kolmogorov turbulence in a random-force-driven Burgers equation: anomalous scaling and probability density functions. Phys. Rev. E (3) 52 (1995), no. 5, part B, 5681--5684. MR1385911 (97b:76073)

  7. Cuerno, Z.R.; Barab'{a}si, A.-L.. Dynamic scaling of ion-sputtered surfaces. Phys. Rev. Lett. 74 (1995), 4746--4749. Math. Review number not available.

  8. M. C. Cross; P. C. Hohenberg. Pattern formation out side of equilibrium. Rev. Mod. Phys. 65 (1993), 851--1112. Math. Review number not available.

  9. de Bouard, A.; Debussche, A. Random modulation of solitons for the stochastic Korteweg-de Vries equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 2, 251--278. MR2310695 (2008i:60103)
  10. 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 (95g:60073)
  11. Da Prato, G.; Kwapień, S.; Zabczyk, J. Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics 23 (1987), no. 1, 1--23. MR0920798 (89b:60148)
  12. Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido. The dynamics of modulated wave trains. Mem. Amer. Math. Soc. 199 (2009), no. 934, viii+105 pp. ISBN: 978-0-8218-4293-5 MR2507940
  13. A. Hutt.. Additive noise may change the stability of nonlinear systems. Europhys. Lett. 84 (2008), 34003. Math. Review number not available.

  14. A. Hutt; A. Longtin; L. Schimansky-Geier. Additive global noise delays Turing bifurcations. Physical Review Letters 98 (2007), 230601. Math. Review number not available.

  15. Hutt, Axel; Longtin, Andre; Schimansky-Geier, Lutz. Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation. Phys. D 237 (2008), no. 6, 755--773. MR2452166 (2009m:60100)

  16. Kirrmann, Pius; Schneider, Guido; Mielke, Alexander. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A 122 (1992), no. 1-2, 85--91. MR1190233 (93i:35132)
  17. K.B. Lauritsen; R. Cuerno; H.A. Makse. Noisy Kuramoto-Sivashinsky equation for an erosion model. Phys. Rev. E 54 (1996), 3577--3580. Math. Review number not available.

  18. Liu, Kai. Stability of infinite dimensional stochastic differential equations with applications. Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 135. Chapman & Hall/CRC, Boca Raton, FL, 2006. xii+298 pp. ISBN: 978-1-58488-598-6; 1-58488-598-X MR2165651 (2006f:60060)
  19. M. Raible; S.G. Mayr; S.J. Linz; M. Moske; P. Hänggi; K. Samwer. Amorphous thin film growth: Theory compared with experiment. Europhysics Letters 50 (2000), 61--67. Math. Review number not available.

  20. Roberts, A. J. A step towards holistic discretisation of stochastic partial differential equations. ANZIAM J. 45 (2003/04), (C), C1--C15. MR2180921 (2006k:65015)
  21. A.J. Roberts; Wei Wang. Macroscopic reduction for stochastic reaction-diffusion equations. Preprint (2008), arXiv:0812.1837v1 [math-ph].

  22. Schneider, Guido. The validity of generalized Ginzburg-Landau equations. Math. Methods Appl. Sci. 19 (1996), no. 9, 717--736. MR1391402 (97a:35221)
  23. D. Siegert; M. Plischke. Solid-on-solid models of molecular-beam epitaxy. Physics Rev. E 50 (1994), 917-931. Math. Review number not available.

  24. Schneider, Guido; Uecker, Hannes. The amplitude equations for the first instability of electro-convection in nematic liquid crystals in the case of two unbounded space directions. Nonlinearity 20 (2007), no. 6, 1361--1386. MR2327129 (2008i:76080)
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