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Dissertation/Thesis Abstract

Results on the Parabolic Anderson Model
by Rael, Michael Brian, Ph.D., University of California, Irvine, 2013, 49; 3562176
Abstract (Summary)

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 O1/3) 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.

Indexing (document details)
Advisor: Cranston, Michael
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
Publication Number: 3562176
ISBN: 978-1-303-09720-1
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