Analysis of multiscale methods for stochastic differential equations

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Diffusion approximation for fully coupled stochastic differential equations (2020, unknown): “[6, 7, 15, 26].”
Strong and weak orders in averaging for SPDEs (2012, methodology): “Convergence in law or in probability of X ε to X in the space C([0, T ], H) can be shown by different techniques: by using a Khasminskii technique based on a subdivision of the interval [0, T ](see [19,15]); a Poisson equation (see [18]); the method of perturbed test functions and of a martingale pr”
S-ROCK methods for stiff Ito SDEs (2008, background): “…Edinburgh EH9 3JZ, UK, a.abdulle@ed.ac.uk †LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China, tieli@pku.edu.cn 1 where Inl = Wl(tn+1) − Wl(tn) are independent Wiener increments drawn from the normal distributions with zero mean and variance h = tn+1 − tn.”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, unknown): “…mechanical system: Kapitza’s inverted pendulum 43 6.7 Nonautonomous SDE system with hidden slow variables . . . . . . . . . . 45 6.8 Langevin equations with slow noise and friction . . . . . . . . . . . . . . . 46 6.9 Langevin equations with fast noise and friction . . . . . . . . . . . . . . . 48”