Type of Document Dissertation Author Buterakos, Lewis Allen URN etd-08182003-173249 Title The Exit Time Distribution for Small Random Perturbations of Dynamical Systems with a Repulsive Type Stationary Point Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Day, Martin V. Committee Chair Ball, Joseph A. Committee Member Boisen, Monte B. Jr. Committee Member Kohler, Werner E. Committee Member Rossi, John F. Committee Member Keywords

- repulsive stationary point
- dynamical systems
- asymptotics
- random perturbations
- stochastic differential equations
Date of Defense 2003-08-04 Availability unrestricted 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.

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