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Propagating lyapunov functions to prove noise-induced stabilization

dc.contributor.author Athreyaz, A
dc.contributor.author Kolba, T
dc.contributor.author Mattingly, Jonathan Christopher
dc.date.accessioned 2015-03-20T17:52:24Z
dc.date.issued 2012-11-19
dc.identifier.uri https://hdl.handle.net/10161/9518
dc.description.abstract We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the addition of additive noise in the vertical direction leads to a unique invariant probability measure to which the system converges at a uniform, exponential rate. These facts are established primarily through the construction of a Lyapunov function which we generate as the solution to a sequence of Poisson equations. Unlike a number of other works, however, our Lyapunov function is constructed in a systematic way, and we present a meta-algorithm we hope will be applicable to other problems. We conclude by proving positivity properties of the transition density by using Malliavin calculus via some unusually explicit calculations.
dc.relation.ispartof Electronic Journal of Probability
dc.relation.isversionof 10.1214/EJP.v17-2410
dc.title Propagating lyapunov functions to prove noise-induced stabilization
dc.type Journal article
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 17
dc.identifier.eissn 1083-6489


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