Free access
Issue
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 1135 - 1153
DOI http://dx.doi.org/10.1051/m2an/2010055
Published online 26 August 2010
  1. I. Babuška and M. Suri, The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev. 36 (1994) 578–632. [CrossRef] [MathSciNet]
  2. I. Babuška, R. Tempone and G.E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 (2004) 800–825. [CrossRef] [MathSciNet]
  3. R.H. Cameron and W.T. Martin, The orthogonal development of nonlinear functionals in a series of Fourier-Hermite functions. Ann. Math. 48 (1947) 385–392. [CrossRef]
  4. Y. Cao, On convergence rate of Wiener-Ito expansion for generalized random variables. Stochastics 78 (2006) 179–187. [MathSciNet]
  5. P.G. Ciarlet, The finite element method for elliptic problems, Classics in Applied Mathematics 40. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2002).
  6. F.W. Elliott, Jr., D.J. Horntrop and A.J. Majda, A Fourier-wavelet Monte Carlo method for fractal random fields. J. Comput. Phys. 132 (1997) 384–408. [CrossRef] [MathSciNet]
  7. T. Hida, H.-H. Kuo, J. Potthoff and L. Sreit, White noise. Kluwer Academic Publishers, Boston (1993).
  8. H. Holden, B. Øksendal, J. Ubøe and T. Zhang, Stochastic partial differential equations. Birkhäuser, Boston (1996).
  9. K. Itô, Stochastic integral. Proc. Imp. Acad. Tokyo 20 (1944) 519–524. [CrossRef] [MathSciNet]
  10. G.E. Karniadakis and S.J. Sherwin, Spectral/hp element methods for computational fluid dynamics. Second edition, Numerical Mathematics and Scientific Computation, Oxford University Press, New York (2005).
  11. Yu.G. Kondratiev, P. Leukert, J. Potthoff, L. Streit and W. Westerkamp, Generalized functionals in Gaussian spaces: the characterization theorem revisited. J. Funct. Anal. 141 (1996) 301–318. [CrossRef] [MathSciNet]
  12. H.-H. Kuo, White noise distribution theory. Probability and Stochastics Series, CRC Press, Boca Raton (1996).
  13. M. Loève, Probability theory – I, Graduate Texts in Mathematics 45. Fourth edition, Springer-Verlag, New York (1977).
  14. S.V. Lototsky and B.L. Rozovskii, Stochastic differential equations driven by purely spatial noise. SIAM J. Math. Anal. 41 (2009) 1295–1322. [CrossRef] [MathSciNet]
  15. D. Nualart, The Malliavin calculus and related topics. Second edition, Probability and its Applications (New York), Springer-Verlag, Berlin (2006).
  16. S. Pilipović and D. Seleši, Expansion theorems for generalized random processes, Wick products and applications to stochastic differential equations. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 (2007) 79–110. [CrossRef] [MathSciNet]
  17. S. Pilipović and D. Seleši, On the generalized stochastic Dirichlet problem. Part I: The stochastic weak maximum principle. Potential Anal. 32 (2010) 363–387. [CrossRef] [MathSciNet]
  18. Ch. Schwab, p- and hp-finite element methods, Theory and applications in solid and fluid mechanics. Numerical Mathematics and Scientific Computation, Oxford University Press, New York (1998).
  19. M. Shinozuka and G. Deodatis, Simulation of stochastic processes by spectral representation. AMR 44 (1991) 191–204. [MathSciNet]
  20. T.G. Theting, Solving Wick-stochastic boundary value problems using a finite element method. Stochastics Stochastics Rep. 70 (2000) 241–270. [MathSciNet]
  21. G. Våge, Variational methods for PDEs applied to stochastic partial differential equations. Math. Scand. 82 (1998) 113–137. [MathSciNet]
  22. X. Wan, B. Rozovskii and G.E. Karniadakis, A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus. Proc. Natl. Acad. Sci. USA 106 (2009) 14189–14194. [CrossRef] [MathSciNet]

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