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dc.contributor.authorBudhiraja, Amarjiten_US
dc.contributor.authorDupuis, Paulen_US
dc.contributor.authorSalins, Michaelen_US
dc.date.accessioned2019-04-22T18:32:58Z
dc.date.available2019-04-22T18:32:58Z
dc.date.issued2018-03-05
dc.identifierhttp://arxiv.org/abs/1803.00648v1
dc.identifier.citationAmarjit Budhiraja, Paul Dupuis, Michael Salins. "Uniform large deviation principles for Banach space valued stochastic differential equations."
dc.identifier.urihttps://hdl.handle.net/2144/34887
dc.description.abstractWe prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key step in the proof is showing that a uniform large deviation principle over compact sets is implied by a uniform over compact sets Laplace principle. Because bounded subsets of infinite dimensional Banach spaces are in general not relatively compact in the norm topology, we embed the Banach space into its double dual and utilize the weak-$\star $ compactness of closed bounded sets in the double dual space. We prove that a modified version of our stochastic differential equation satisfies a uniform Laplace principle over weak-$\star $ compact sets and consequently a uniform over bounded sets large deviation principle. We then transfer this result back to the original equation using a contraction principle. The main motivation for this uniform LDP is to generalize results of Freidlin and Wentzell concerning the behavior of finite dimensional SDEs. Here we apply the uniform LDP to study the asymptotics of exit times from bounded sets of Banach space valued small noise SDE, including reaction diffusion equations with multiplicative noise and $2$-dimensional stochastic Navier-Stokes equations with multiplicative noise.en_US
dc.subjectMathematicsen_US
dc.subjectProbabilityen_US
dc.subjectUniform large deviationsen_US
dc.subjectVariational representationsen_US
dc.subjectUniform Laplace principleen_US
dc.subjectStochastic partial differential equationsen_US
dc.subjectSmall noise asymptoticsen_US
dc.subjectExit-time asymptoticsen_US
dc.subjectStochastic reaction-diffusion equationsen_US
dc.subjectStochasic Navier-Stokes equationen_US
dc.titleUniform large deviation principles for Banach space valued stochastic differential equationsen_US
dc.typeArticleen_US
dc.description.versionFirst author draften_US
pubs.elements-sourcearxiven_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


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