dc.contributor.author Budhiraja, Amarjit en_US dc.contributor.author Dupuis, Paul en_US dc.contributor.author Salins, Michael en_US dc.date.accessioned 2019-04-22T18:32:58Z dc.date.available 2019-04-22T18:32:58Z dc.date.issued 2018-03-05 dc.identifier http://arxiv.org/abs/1803.00648v1 dc.identifier.citation Amarjit Budhiraja, Paul Dupuis, Michael Salins. "Uniform large deviation principles for Banach space valued stochastic differential equations." dc.identifier.uri https://hdl.handle.net/2144/34887 dc.description.abstract We 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.subject Mathematics en_US dc.subject Probability en_US dc.subject Uniform large deviations en_US dc.subject Variational representations en_US dc.subject Uniform Laplace principle en_US dc.subject Stochastic partial differential equations en_US dc.subject Small noise asymptotics en_US dc.subject Exit-time asymptotics en_US dc.subject Stochastic reaction-diffusion equations en_US dc.subject Stochasic Navier-Stokes equation en_US dc.title Uniform large deviation principles for Banach space valued stochastic differential equations en_US dc.type Article en_US dc.description.version First author draft en_US pubs.elements-source arxiv en_US pubs.notes Embargo: Not known en_US pubs.organisational-group Boston University en_US pubs.organisational-group Boston University, College of Arts & Sciences en_US pubs.organisational-group Boston University, College of Arts & Sciences, Department of Mathematics & Statistics en_US
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