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The stochastic exit problem for dynamical systems

Citation

Williams, Randall Gary (1978) The stochastic exit problem for dynamical systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:03212013-095136861

Abstract

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Franklin, Joel N.
Thesis Committee:
  • Unknown, Unknown
Defense Date:22 June 1977
Record Number:CaltechTHESIS:03212013-095136861
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:03212013-095136861
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7540
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:21 Mar 2013 18:24
Last Modified:21 Mar 2013 18:24

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