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Sensitivity to switching rates in stochastically switched ODEs

dc.contributor.author Lawley, SD
dc.contributor.author Mattingly, Jonathan Christopher
dc.contributor.author Reed, Michael C
dc.date.accessioned 2015-03-20T17:49:55Z
dc.date.issued 2014-01-01
dc.identifier.issn 1539-6746
dc.identifier.uri http://hdl.handle.net/10161/9515
dc.description.abstract We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.
dc.relation.ispartof Communications in Mathematical Sciences
dc.relation.isversionof 10.4310/CMS.2014.v12.n7.a9
dc.title Sensitivity to switching rates in stochastically switched ODEs
dc.type Journal article
pubs.begin-page 1343
pubs.end-page 1352
pubs.issue 7
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 12
dc.identifier.eissn 1945-0796


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