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 O(κ1/3) near 0. We prove the required upper bound, the lower bound having been proven in (Cranston & Mountford 2006).
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.
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.
|Commitee:||Klein, Abel, Solna, Knut|
|School:||University of California, Irvine|
|Department:||Mathematics - Ph.D.|
|School Location:||United States -- California|
|Source:||DAI-B 74/09(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Lyapunov exponent, Parabolic Anderson models, Stratonovich differential|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be