We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. The result is proven by using Lyapunov functions and geometric control theory.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/145150 |
| Date | January 2011 |
| Creators | Herzog, David Paul |
| Contributors | Wehr, Jan, Kennedy, Thomas G, Bhattacharya, Rabindra, Watkins, Joseph C |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Electronic Dissertation, text |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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