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Large deviations technique on stochastic reaction-diffusion equations
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Xu, Lu (2008) Large deviations technique on stochastic reaction-diffusion equations. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2317741~S1
Abstract
There are two different problems studied in this thesis. The first one is a travelling wave problem. We will improve the result proved in [4] to derive the ergodic property of the travelling wave behind the wavefront. The second problem is a large deviation problem concerning solutions to certain kind stochastic partial differential equations. We will first briefly introduce some basics about SPDE in chapter 2. In chapter 3, we will prove a large deviation principle for super-Brownian motion when it is considered as a solution to an SPDE, using the LDP for super-Brownian motion when it is considered as a measure-valued branching process as solution to a martingale problem. In chapter 4, we will prove another LDP result for solutions of a stochastic reaction-diffusion equation with degenerate noise term. Finally in chapter 5, we will explore some applications of those LDP results proved previously.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Large deviations -- Research, Stochastic partial differential equations, Brownian motion processes, Degenerate differential equations | ||||
Official Date: | October 2008 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Tribe, Roger | ||||
Format of File: | |||||
Extent: | 130 leaves | ||||
Language: | eng |
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