# American Institute of Mathematical Sciences

January  2016, 36(1): 481-497. doi: 10.3934/dcds.2016.36.481

## Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus

 1 School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China

Received  August 2014 Revised  March 2015 Published  June 2015

This paper deals with the weak error estimates of the exponential Euler method for semi-linear stochastic partial differential equations (SPDEs). A weak error representation formula is first derived for the exponential integrator scheme in the context of truncated SPDEs. The obtained formula that enjoys the absence of the irregular term involved with the unbounded operator is then applied to a parabolic SPDE. Under certain mild assumptions on the nonlinearity, we treat a full discretization based on the spectral Galerkin spatial approximation and provide an easy weak error analysis, which does not rely on Malliavin calculus.
Citation: Xiaojie Wang. Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 481-497. doi: 10.3934/dcds.2016.36.481
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