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Type: Journal article
Title: Average and deviation for slow-fast stochastic partial differential equations
Author: Wang, W.
Roberts, A.
Citation: Journal of Differential Equations, 2012; 253(5):1265-1286
Publisher: Academic Press Inc
Issue Date: 2012
ISSN: 0022-0396
Department: Faculty of Engineering, Computer & Mathematical Sciences
Statement of
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
Rights: Copyright © 2012 Elsevier Inc. Published by Elsevier Inc. All rights reserved.
DOI: 10.1016/j.jde.2012.05.011
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Appears in Collections:Applied Mathematics publications
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