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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

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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 or Dissertation (PhD)
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:
DateEvent
October 2008Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Tribe, Roger
Format of File: pdf
Extent: 130 leaves
Language: eng

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