A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations
发布时间：2020-06-28
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发表刊物：Applied Numerical Mathematics
关键字：Stochastic partial differential equations; Invariant measure; Ergodicity; Weak approximation; Exponential Euler scheme
摘要：We discrete the ergodic semilinear stochastic partial differential equations in space dimension d ≤3with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the spatial semi-discretization and the spatio-temporal full discretization are ergodic. Further, convergence orders of the numerical invariant measures, depending on the regularity of noise, are recovered based on an easy time-independent weak error analysis without relying on Malliavin calculus. To be precise, the convergence order is 1-epsilon in space and 1/2-epsilon in time for the space-time white noise case and 2 -epsilon in space and 1-epsilon in time for the trace class noise case in space dimension d =1, with arbitrarily small epsilon>0. Numerical results are finally reported to confirm these theoretical findings.
合写作者：Chen Ziheng, Gan Siqing, Wang Xiaojie
论文类型：期刊论文
文献类型：J
卷号：157
页面范围：135–158
是否译文：否
发表时间：2020-06-15
收录刊物：SCI