Average and deviation for slow-fast stochastic partial differential equations

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2012

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Wang, W.
Roberts, A.

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Journal article

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Journal of Differential Equations, 2012; 253(5):1265-1286

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W. Wang, A.J. Roberts

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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.

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Copyright © 2012 Elsevier Inc. Published by Elsevier Inc. All rights reserved.

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