Invariant densities for dynamical systems with random switching

dc.contributor.advisor Bakhtin, Yuri
dc.contributor.author Hurth, Tobias
dc.contributor.committeeMember Bunimovich, Leonid
dc.contributor.committeeMember de la Llave, Rafael
dc.contributor.committeeMember Koltchinskii, Vladimir
dc.contributor.committeeMember Popescu, Ionel
dc.contributor.committeeMember Mattingly, Jonathan C.
dc.contributor.department Mathematics
dc.date.accessioned 2014-08-27T13:38:35Z
dc.date.available 2014-08-27T13:38:35Z
dc.date.created 2014-08
dc.date.issued 2014-06-19
dc.date.submitted August 2014
dc.date.updated 2014-08-27T13:38:35Z
dc.description.abstract We studied invariant measures and invariant densities for dynamical systems with random switching (switching systems, in short). These switching systems can be described by a two-component Markov process whose first component is a stochastic process on a finite-dimensional smooth manifold and whose second component is a stochastic process on a finite collection of smooth vector fields that are defined on the manifold. We identified sufficient conditions for uniqueness and absolute continuity of the invariant measure associated to this Markov process. These conditions consist of a Hoermander-type hypoellipticity condition and a recurrence condition. In the case where the manifold is the real line or a subset of the real line, we studied regularity properties of the invariant densities of absolutely continuous invariant measures. We showed that invariant densities are smooth away from critical points of the vector fields. Assuming in addition that the vector fields are analytic, we derived the asymptotically dominant term for invariant densities at critical points.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/52274
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Randomly switched ODEs
dc.subject Piecewise deterministic Markov processes
dc.subject Invariant densities
dc.subject Hypoellipticity
dc.title Invariant densities for dynamical systems with random switching
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level Doctoral
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