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Stochastic switching in infinite dimensions with applications to random parabolic PDE

dc.contributor.author Lawley, SD
dc.contributor.author Mattingly, Jonathan Christopher
dc.contributor.author Reed, Michael C
dc.date.accessioned 2015-03-20T17:51:38Z
dc.date.issued 2015-01-01
dc.identifier.issn 0036-1410
dc.identifier.uri http://hdl.handle.net/10161/9517
dc.description.abstract © 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.
dc.relation.ispartof SIAM Journal on Mathematical Analysis
dc.relation.isversionof 10.1137/140976716
dc.title Stochastic switching in infinite dimensions with applications to random parabolic PDE
dc.type Journal article
pubs.begin-page 3035
pubs.end-page 3063
pubs.issue 4
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Statistical Science
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 47
dc.identifier.eissn 1095-7111


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