ANALYSIS OF AN HMM TIME-DISCRETIZATION SCHEME FOR A SYSTEM OF STOCHASTIC PDEs

作者：Brehier Charles Edouard^*

来源：SIAM Journal on Numerical Analysis, 2013, 51(2): 1185-1210.

DOI：10.1137/110853078

• stochastic partial differential equations
• heterogeneous multiscale method
• time scale separation
• Euler scheme
• strong and weak approximation

We consider the discretization in time of a system of parabolic stochastic partial differential equations with slow and fast components; the fast equation is driven by an additive space-time white noise. The numerical method is inspired by the averaging principle satisfied by this system and fits to the framework of heterogeneous multiscale methods. The slow and the fast components are approximated with two coupled numerical semi-implicit Euler schemes depending on two different time step sizes. We derive bounds of the approximation error on the slow component in the strong sense-approximation of trajectories-and in the weak sense-approximation of the laws. The estimates generalize the results of [W. E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58 (2005), pp. 1544-1585] in the case of infinite dimensional processes.

• 出版日期2013