Effectiveness of implicit methods for stiff stochastic differential equations, Commun. Comput. Phys, vol.3, issue.2, pp.295-307, 2008. ,
Random Dynamical Systems, 1998. ,
Handbook of Brownian motion: Facts and formulae, 2002. ,
Approximation of the invariant measure via a Euler scheme for stochastic PDEs driven by space-time white noise ,
Analysis of a HMM discretization scheme for SPDEs ,
Markov chains Gibbs fields, Monte Carlo simulation, and queues, Texts in Applied Mathematics, 1999. ,
Functional analysisAnalyse fonctionnelle, Théorie et applications.). Collection Mathématiques Appliquées pour la Maîtrise. Paris: Masson. 248 p, 1994. ,
Second order PDE's in finite and infinite dimension, Lecture Notes in Mathematics, vol.1762, 2001. ,
DOI : 10.1007/b80743
A Khasminskii type averaging principle for stochastic reaction???diffusion equations, The Annals of Applied Probability, vol.19, issue.3, pp.899-948, 2009. ,
DOI : 10.1214/08-AAP560
Normal deviations from the averaged motion for some reaction???diffusion equations with fast oscillating perturbation, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.6, pp.614-647, 2009. ,
DOI : 10.1016/j.matpur.2009.04.007
Averaging principle for a class of stochastic reaction???diffusion equations, Probability Theory and Related Fields, vol.17, issue.1-2, pp.137-177, 2009. ,
DOI : 10.1007/s00440-008-0144-z
On the discretization in time of semilinear parabolic equations with nonsmooth initial data, Mathematics of Computation, vol.49, issue.180, pp.359-377, 1987. ,
DOI : 10.1090/S0025-5718-1987-0906176-3
Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and Its Applications . 44. Cambridge etc, 1992. ,
Ergodicity for infinite dimensional systems, London Mathematical Society Lecture Note Series, vol.229, issue.339, 1996. ,
DOI : 10.1017/CBO9780511662829
Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations, Mathematics of Computation, vol.70, issue.233, pp.121-134, 2001. ,
DOI : 10.1090/S0025-5718-00-01224-2
Weak approximation of stochastic partial differential equations: the nonlinear case, Mathematics of Computation, vol.80, issue.273, pp.89-117, 2011. ,
DOI : 10.1090/S0025-5718-2010-02395-6
Ergodic BSDEs under weak dissipative assumptions, Stochastic Processes and their Applications, pp.407-426, 2011. ,
DOI : 10.1016/j.spa.2010.11.009
URL : https://hal.archives-ouvertes.fr/hal-00472146
Weak order for the discretization of the stochastic heat equation, Mathematics of Computation, vol.78, issue.266, pp.845-863, 2009. ,
DOI : 10.1090/S0025-5718-08-02184-4
URL : https://hal.archives-ouvertes.fr/hal-00183249
Expose de la théorie des chaînes simples constantes de Markoff à un nombre fini d'etats, Rev. Math. Union Interbalkan, vol.2, pp.77-105, 1938. ,
DOI : 10.24033/asens.883
The heterogeneous multiscale methods, Commun. Math. Sci, vol.1, issue.1, pp.87-132, 2003. ,
Heterogeneous multiscale methods: a review, Commun. Comput. Phys, vol.2, issue.3, pp.367-450, 2007. ,
Analysis of multiscale methods for stochastic differential equations, Commun. Pure Appl. Math, vol.58, issue.11, pp.1544-1585, 2005. ,
Partial Differential Equations, Graduate Studies in Mathematics, vol.19, 2010. ,
Analysis of splitting methods for reaction-diffusion problems using stochastic calculus, Mathematics of Computation, vol.78, issue.267, pp.1467-1483, 2009. ,
DOI : 10.1090/S0025-5718-08-02185-6
URL : https://hal.archives-ouvertes.fr/hal-00777649
A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes, Communications in Computational Physics, 2000. ,
DOI : 10.4208/cicp.070709.011209a
Wave propagation and time reversal in randomly layered media. Stochastic Modelling and Applied Probability 56, p.612, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00172124
Random perturbations of dynamical systems. Transl. from the Russian by Joseph Szuecs, 1998. ,
Strong convergence in stochastic averaging principle for two time-scales stochastic partial differential equations, Journal of Mathematical Analysis and Applications, vol.384, issue.1, pp.70-86, 2011. ,
DOI : 10.1016/j.jmaa.2011.02.076
Euler schemes and half-space approximation for the simulation of diffusion in a domain, ESAIM: Probability and Statistics, vol.5, pp.261-297, 2001. ,
DOI : 10.1051/ps:2001112
An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.44-47, 2006. ,
DOI : 10.1016/j.cma.2005.10.010
Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I. Potential Anal, pp.1-25, 1998. ,
Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise, Potential Analysis, vol.11, issue.1, pp.1-37, 1999. ,
DOI : 10.1023/A:1008699504438
Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise. Potential Anal, pp.725-757, 1997. ,
On an averaging principle for Itô stochastic differential equations, Kibernetica, issue.4, pp.260-279, 1968. ,
Limit behavior of two-time-scale diffusions revisited, Journal of Differential Equations, vol.212, issue.1, pp.85-113, 2005. ,
DOI : 10.1016/j.jde.2004.08.013
Approximation for semilinear stochastic evolution equations. Potential Anal, pp.141-186, 2003. ,
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Processes and their Applications, vol.101, issue.2, pp.185-232, 2002. ,
DOI : 10.1016/S0304-4149(02)00150-3
On a variance reduction technique for micro???macro simulations of polymeric fluids, Journal of Non-Newtonian Fluid Mechanics, vol.122, issue.1-3, pp.1-3, 2004. ,
DOI : 10.1016/j.jnnfm.2003.09.006
Equation-free, coarsegrained multiscale computation: enabling microscopic simulators to perform system-level tasks, Communications in Mathematical Sciences, vol.1, issue.4, pp.715-762, 2003. ,
Numerical solution of stochastic differential equations, Applications of Mathematics, vol.23, 1992. ,
A Coupling Approach??to Randomly Forced Nonlinear PDE's. I, Communications in Mathematical Physics, vol.221, issue.2, pp.351-366, 2001. ,
DOI : 10.1007/s002200100479
Semidiscretization in Time for Parabolic Problems, Mathematics of Computation, vol.33, issue.147, pp.919-931, 1979. ,
DOI : 10.2307/2006068
A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations, SIAM Journal on Scientific Computing, vol.35, issue.4 ,
DOI : 10.1137/120872681
URL : https://hal.archives-ouvertes.fr/hal-00691939
Strong convergence of principle of averaging for multiscale stochastic dynamical systems, Communications in Mathematical Sciences, vol.8, issue.4, pp.999-1020, 2010. ,
DOI : 10.4310/CMS.2010.v8.n4.a11
Absorbing boundaries and optimal stopping in a stochastic differential equation, Physics Letters A, vol.254, issue.5, pp.257-262, 1999. ,
DOI : 10.1016/S0375-9601(99)00117-6
Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Communications in Mathematical Physics, vol.230, issue.3, pp.421-462, 2002. ,
DOI : 10.1007/s00220-002-0688-1
Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations, SIAM Journal on Numerical Analysis, vol.48, issue.2, pp.552-577, 2010. ,
DOI : 10.1137/090770527
Markov chains and stochastic stability, 2009. ,
Numerical integration of stochastic differential equations. Transl. from the Russian Mathematics and its Applications (Dordrecht). 313, 1994. ,
Stochastic numerics for mathematical physics. Scientific Computation, 2004. ,
DOI : 10.1007/978-3-662-10063-9
The Malliavin calculus and related topics, 2006. ,
DOI : 10.1007/978-1-4757-2437-0
Multiscale methods. Averaging and homogenization, Texts in Applied Mathematics 53, 2008. ,
On the discretization in time of parabolic stochastic partial differential equations, Monte Carlo Methods Appl, vol.7, issue.3-4, pp.359-368, 2001. ,
Malliavin calculus with applications to stochastic partial differential equations, Fundamental Sciences: Mathematics . Boca Raton, vol.162, 2005. ,
DOI : 10.1201/9781439818947
Hopf bifurcation of the unsteady regularized driven cavity flow, Journal of Computational Physics, vol.95, issue.1, pp.228-245, 1991. ,
DOI : 10.1016/0021-9991(91)90261-I
Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution. (Discretization of a stochastic differential equation and computation of expectations of functions of the solution), 1986. ,
DOI : 10.1051/m2an/1986200101411
URL : http://archive.numdam.org/article/M2AN_1986__20_1_141_0.pdf
Second-order discretization schemes of stochastic differential systems for the computation of the invariant law, Stochastics and Stochastic Reports, vol.20, issue.1, pp.13-36, 1990. ,
DOI : 10.1080/17442509008833606
URL : https://hal.archives-ouvertes.fr/inria-00075799
Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Analysis and Applications, vol.20, issue.4, pp.483-509, 1990. ,
DOI : 10.1080/07362999008809220
URL : https://hal.archives-ouvertes.fr/inria-00075490
Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 2001. ,
DOI : 10.1115/1.3424338
Numerical Techniques for Multi-Scale Dynamical Systems with Stochastic Effects, Communications in Mathematical Sciences, vol.1, issue.2, pp.385-391, 2003. ,
DOI : 10.4310/CMS.2003.v1.n2.a11
Finite element methods for parabolic stochastic PDE's. Potential Anal, pp.1-43, 2005. ,
DOI : 10.1007/s11118-004-2950-y