Wang, W.Roberts, A.2012-06-072012-06-072012Journal of Differential Equations, 2012; 253(5):1265-12860022-03961090-2732http://hdl.handle.net/2440/71453Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any Lipschitz assumption on the slow modes. The rate of convergence in probability is obtained as a byproduct. Importantly, the stochastic deviation between the original equation and the averaged equation is also studied. A martingale approach proves that the deviation is described by a Gaussian process. This gives an approximation to errors of order O(ε) instead of order O(√ε) attained in previous averaging.enCopyright © 2012 Elsevier Inc. Published by Elsevier Inc. All rights reserved.slow-fast stochastic partial differential equationsaveragingmartingaleJournal article00201194072012060713374110.1016/j.jde.2012.05.01197 Expanding Knowledge9701 Expanding Knowledge970101 Expanding Knowledge in the Mathematical Sciences01 Mathematical Sciences0102 Applied Mathematics010201 Approximation Theory and Asymptotic Methods010204 Dynamical Systems in Applications0003055897000012-s2.0-8486194337524371Roberts, A. [0000-0001-8930-1552]