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

We 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2003

Author dc:creator

• Buterakos, Lewis Allen

Chair dc:contributor.committeechair

• Day, Martin V.

Committee members dc:contributor.committeemember

• Boisen, Monte B. Jr.
• Rossi, John F.
• Ball, Joseph A.
• Kohler, Werner E.

• repulsive stationary point
• dynamical systems
• asymptotics
• random perturbations
• stochastic differential equations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-08182003-173249

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28703