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|Title:||Average and deviation for slow-fast stochastic partial differential equations|
|Citation:||Journal of Differential Equations, 2012; 253(5):1265-1286|
|Publisher:||Academic Press Inc|
|Department:||Faculty of Engineering, Computer & Mathematical Sciences|
|W. Wang, A.J. Roberts|
|Abstract:||Averaging 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.|
|Keywords:||slow-fast stochastic partial differential equations; averaging; martingale|
|Rights:||Copyright © 2012 Elsevier Inc. Published by Elsevier Inc. All rights reserved.|
|Appears in Collections:||Applied Mathematics publications|
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