Average and deviation for slow-fast stochastic partial differential equations

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dc.contributor.authorWang, W.
dc.contributor.authorRoberts, A.
dc.contributor.departmentFaculty of Engineering, Computer & Mathematical Sciences
dc.date.issued2012
dc.description.abstractAveraging 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.
dc.description.statementofresponsibilityW. Wang, A.J. Roberts
dc.identifier.citationJournal of Differential Equations, 2012; 253(5):1265-1286
dc.identifier.doi10.1016/j.jde.2012.05.011
dc.identifier.issn0022-0396
dc.identifier.issn1090-2732
dc.identifier.orcidRoberts, A. [0000-0001-8930-1552]
dc.identifier.urihttp://hdl.handle.net/2440/71453
dc.language.isoen
dc.publisherAcademic Press Inc
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0774311
dc.relation.granthttp://purl.org/au-research/grants/arc/DP0774311
dc.rightsCopyright © 2012 Elsevier Inc. Published by Elsevier Inc. All rights reserved.
dc.source.urihttps://doi.org/10.1016/j.jde.2012.05.011
dc.subjectslow-fast stochastic partial differential equations
dc.subjectaveraging
dc.subjectmartingale
dc.titleAverage and deviation for slow-fast stochastic partial differential equations
dc.typeJournal article
pubs.publication-statusPublished

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