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dc.contributor.authorHu, Wenqingen_US
dc.contributor.authorSalins, Michaelen_US
dc.contributor.authorSpiliopoulos, Konstantinosen_US
dc.date.accessioned2019-04-22T18:25:48Z
dc.date.available2019-04-22T18:25:48Z
dc.date.issued2017-10-07
dc.identifierhttp://arxiv.org/abs/1710.02618v1
dc.identifier.citationWenqing Hu, Michael Salins, Konstantinos Spiliopoulos. 2017. "Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations."
dc.identifier.urihttps://hdl.handle.net/2144/34886
dc.description.abstractWe study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to characterize the limiting process via a "viable pair" that captures the limiting controlled dynamics and the effective invariant measure simultaneously. The characterization of the limit of the controlled slow-fast processes in terms of viable pair enables us to obtain a variational representation of the large deviation action functional. Due to the infinite--dimensional nature of our set--up, the proof of tightness as well as the analysis of the limit process and in particular the proof of the large deviations lower bound is considerably more delicate here than in the finite--dimensional situation. Smoothness properties of optimal controls in infinite dimensions (a necessary step for the large deviations lower bound) need to be established. We emphasize that many issues that are present in the infinite dimensional case, are completely absent in finite dimensions.en_US
dc.subjectLarge deviation principleen_US
dc.subjectMathematicsen_US
dc.subjectProbabilityen_US
dc.subjectFreidlin and Wentzell estimatesen_US
dc.subjectAveraged equationen_US
dc.subjectSlow–fast reaction–diffusionen_US
dc.titleLarge deviations and averaging for systems of slow–fast reaction–diffusion equationsen_US
dc.typeArticleen_US
dc.description.versionFirst author draften_US
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusUnpublisheden_US


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