Average and deviation for slow-fast stochastic partial differential equations

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dc.creatorWang, W.
dc.creatorRoberts, A. J.
dc.date2009-04-09
dc.date.accessioned2026-07-07T13:01:54Z
dc.date.available2026-07-07T13:01:54Z
dc.descriptionAveraging 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 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 $\mathcal{O}(\e)$ instead of $\mathcal{O}(\sqrt{\e})$ attained in previous averaging.
dc.description22 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0904.1462
dc.identifierhttp://arxiv.org/abs/0904.1462
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226307
dc.subjectAnalysis of PDEs
dc.subjectProbability
dc.titleAverage and deviation for slow-fast stochastic partial differential equations
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