EDP Sciences Journals List
Free access article

Issue ESAIM: M2AN
Volume 35, Number 6, November-December 2001
Page(s) 1055 - 1078
DOI 10.1051/m2an:2001148

References

1
A. Bensoussan and R. Temam, Équations stochastiques du type Navier-Stoke. J. Funct. Anal. 13 (1973) 195-222.
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.
3
C. Cardon-Weber, Autour d'équations aux dérivées partielles stochastiques à dérives non-Lipschitziennes. Thèse, Université Paris VI, Paris (2000).
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.
5
G. Da Prato and A. Debussche, Stochastic Cahn-Hilliard equation. Nonlinear Anal., Theory Methods. Appl. 26 (1996) 241-263.
6
G. Da Prato, A. Debussche and R. Temam, Stochastic Burgers' equation. Nonlinear Differ. Equ. Appl. 1 (1994) 389-402.
7
G. Da Prato and D. Gatarek, Stochastic Burgers equation with correlated noise. Stochastics Stochastics Rep. 52 (1995) 29-41.
8
G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, in Encyclopedia of Mathematics and its Application. Cambridge University Press, Cambridge (1992).
9
F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Relat. Fields 102 (1995) 367-391.
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.
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.
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.
13
I. Gyöngy, Existence and uniqueness results for semilinear stochastic partial differential equations. Stoch. Process Appl. 73 (1998) 271-299.
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.
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).
16
N. Krylov and B.L. Rozovski, Stochastic Evolution equations. J. Sov. Math. 16 (1981) 1233-1277.
17
M.-N. Le Roux, Semidiscretization in Time for Parabolic Problems. Math. Comput. 33 (1979) 919-931.
18
G.N. Milstein, Approximate integration of stochastic differential equations. Theor. Prob. Appl. 19 (1974) 557-562. G.N. Milstein, Weak approximation of solutions of systems of stochastic differential equations. Theor. Prob. Appl. 30 (1985) 750-766.
19
E. Pardoux, Équations aux dérivées partielles stochastiques non linéaires monotones. Étude de solutions fortes de type Ito. Thèse, Université Paris XI, Orsay (1975).
20
B.L. Rozozski, Stochastic evolution equations. Linear theory and application to nonlinear filtering. Kluwer, Dordrecht, The Netherlands (1990).
21
T. Shardlow, Numerical methods for stochastic parabolic PDEs. Numer. Funct. Anal. Optimization 20 (1999) 121-145.
22
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.
23
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.
24
M. Viot, Solutions faibles aux équations aux dérivées partielles stochastiques non linéaires. Thèse, Université Pierre et Marie Curie, Paris (1976).
25
J. B. Walsh, An introduction to stochastic partial differential equations, in Lectures Notes in Mathematics 1180 (1986) 265-437.

Abstract

Copyright EDP Sciences, SMAI 2001



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