Free Access
Issue
ESAIM: M2AN
Volume 35, Number 6, November/December 2001
Page(s) 1055 - 1078
DOI https://doi.org/10.1051/m2an:2001148
Published online 15 April 2002
  1. A. Bensoussan and R. Temam, Équations stochastiques du type Navier-Stoke. J. Funct. Anal. 13 (1973) 195-222. [CrossRef] [Google Scholar]
  2. J.H. Bramble, A.H. Schatz, V. Thomée and L.B. Wahlbin, Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations. SIAM J. Numer. Anal. 14 (1977) 218-241. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Cardon-Weber, Autour d'équations aux dérivées partielles stochastiques à dérives non-Lipschitziennes. Thèse, Université Paris VI, Paris (2000). [Google Scholar]
  4. M. Crouzeix and V. Thomée, On the discretization in time of semilinear parabolic equations with nonsmooth initial data. Math. Comput. 49 (1987) 359-377. [CrossRef] [Google Scholar]
  5. G. Da Prato and A. Debussche, Stochastic Cahn-Hilliard equation. Nonlinear Anal., Theory Methods. Appl. 26 (1996) 241-263. [Google Scholar]
  6. G. Da Prato, A. Debussche and R. Temam, Stochastic Burgers' equation. Nonlinear Differ. Equ. Appl. 1 (1994) 389-402. [CrossRef] [Google Scholar]
  7. G. Da Prato and D. Gatarek, Stochastic Burgers equation with correlated noise. Stochastics Stochastics Rep. 52 (1995) 29-41. [MathSciNet] [Google Scholar]
  8. G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, in Encyclopedia of Mathematics and its Application. Cambridge University Press, Cambridge (1992). [Google Scholar]
  9. F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Relat. Fields 102 (1995) 367-391. [CrossRef] [Google Scholar]
  10. I. Gyöngy, Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I. Potential Anal. 9 (1998) 1-25. [CrossRef] [MathSciNet] [Google Scholar]
  11. I. Gyöngy, Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II. Potential Anal. 11 (1999) 1-37. [CrossRef] [MathSciNet] [Google Scholar]
  12. I. Gyöngy and D. Nualart, Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise. Potential Anal. 7 (1997) 725-757. [CrossRef] [MathSciNet] [Google Scholar]
  13. I. Gyöngy, Existence and uniqueness results for semilinear stochastic partial differential equations. Stoch. Process Appl. 73 (1998) 271-299. [CrossRef] [Google Scholar]
  14. C. Johnson, S. Larsson, V. Thomée and L.B. Wahlbin, Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data. Math. Comput. 49 (1987) 331-357. [CrossRef] [Google Scholar]
  15. P.E. Kloeden and E. Platten, Numerical solution of stochastic differential equations, in Applications of Mathematics 23, Springer-Verlag, Berlin, Heidelberg, New York (1992). [Google Scholar]
  16. N. Krylov and B.L. Rozovski, Stochastic Evolution equations. J. Sov. Math. 16 (1981) 1233-1277. [CrossRef] [Google Scholar]
  17. M.-N. Le Roux, Semidiscretization in Time for Parabolic Problems. Math. Comput. 33 (1979) 919-931. [Google Scholar]
  18. G.N. Milstein, Approximate integration of stochastic differential equations. Theor. Prob. Appl. 19 (1974) 557-562. [Google Scholar]
  19. G.N. Milstein, Weak approximation of solutions of systems of stochastic differential equations. Theor. Prob. Appl. 30 (1985) 750-766. [CrossRef] [Google Scholar]
  20. E. Pardoux, Équations aux dérivées partielles stochastiques non linéaires monotones. Étude de solutions fortes de type Ito. Thèse, Université Paris XI, Orsay (1975). [Google Scholar]
  21. B.L. Rozozski, Stochastic evolution equations. Linear theory and application to nonlinear filtering. Kluwer, Dordrecht, The Netherlands (1990). [Google Scholar]
  22. T. Shardlow, Numerical methods for stochastic parabolic PDEs. Numer. Funct. Anal. Optimization 20 (1999) 121-145. [CrossRef] [Google Scholar]
  23. D. Talay, Efficient numerical schemes for the approximation of expectation of functionals of the solutions of an stochastic differential equation and applications, in Lecture Notes in Control and Information Science 61, Springer, London, (1984) 294-313. [Google Scholar]
  24. D. Talay, Discrétisation d'une équation différentielle stochastique et calcul approché d'espérance de fonctionnelles de la solution. RAIRO Modél. Math. Anal. Numér. 20 (1986) 141-179. [MathSciNet] [Google Scholar]
  25. M. Viot, Solutions faibles aux équations aux dérivées partielles stochastiques non linéaires. Thèse, Université Pierre et Marie Curie, Paris (1976). [Google Scholar]
  26. J. B. Walsh, An introduction to stochastic partial differential equations, in Lectures Notes in Mathematics 1180 (1986) 265-437. [Google Scholar]

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