The Exit Time Distribution for Small Random Perturbations of Dynamical Systems with a Repulsive Type Stationary Point

Simple item page
dc.contributor.authorButerakos, Lewis Allenen
dc.contributor.committeechairDay, Martin V.en
dc.contributor.committeememberBoisen, Monte B. Jr.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberKohler, Werner E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:15:22Zen
dc.date.adate2003-08-22en
dc.date.available2014-03-14T20:15:22Zen
dc.date.issued2003-08-04en
dc.date.rdate2003-08-22en
dc.date.sdate2003-08-18en
dc.description.abstractWe consider a stochastic differential equation on a domain D in n-dimensional real space, where the associated dynamical system is linear, and D contains a repulsive type stationary point at the origin O. We obtain an exit law for the first exit time of the solution process from a ball of arbitrary radius centered at the origin, which involves additive scaling as in Day (1995). The form of the scaling constant is worked out and shown to depend on the structure of the Jordan form of the linear drift. We then obtain an extension of this exit law to the first exit time of the solution process from the general domain D by considering the exit in two stages: first from the origin O to the boundary of the ball, for which the aforementioned exit law applies, and then from the boundary of the ball to the boundary of D. In this way we are able to determine for which Jordan forms we can obtain a limiting distribution for the first exit time to the boundary of D as the noise approaches 0. In particular, we observe there are cases for which the exit time distribution diverges as the noise approaches 0.en
dc.description.degreePh. D.en
dc.identifier.otheretd-08182003-173249en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08182003-173249/en
dc.identifier.urihttp://hdl.handle.net/10919/28703en
dc.publisherVirginia Techen
dc.relation.haspartdissertation.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectrepulsive stationary pointen
dc.subjectdynamical systemsen
dc.subjectasymptoticsen
dc.subjectrandom perturbationsen
dc.subjectstochastic differential equationsen
dc.titleThe Exit Time Distribution for Small Random Perturbations of Dynamical Systems with a Repulsive Type Stationary Pointen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
dissertation.pdf
Size:
643.74 KB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations