<p> In this dissertation we present various results pertaining to the Parabolic Anderson Model. First we show that the Lyapunov exponent, λ(κ), of the Parabolic Anderson Model in continuous space with Stratonovich differential is <i>O</i>(κ<sup>1/3</sup>) near 0. We prove the required upper bound, the lower bound having been proven in (Cranston & Mountford 2006). </p><p> Second, we prove the existence of stationary measures for the Parabolic Anderson Model in continuous space with Ito differential. Furthermore, we prove that these measures are associated and determined by the average mass of the initial configuration. </p><p> Finally we present progress towards computing the Lyapunov exponent of the Quasi-Stationary Parabolic Anderson Model. We prove a smaller upper bound on λ(κ), improving on the work in (Boldrighini, Molchanov, & Pellegrinotti 2007), but our bound is not sharp. Computing λ(κ) in this model remains an open problem.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3562176 |
| Date | 02 July 2013 |
| Creators | Rael, Michael Brian |
| Publisher | University of California, Irvine |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
Page generated in 0.0016 seconds