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dc.contributor.authorDriver, David Philip
dc.date.accessioned2018-07-03T14:24:11Z
dc.date.available2018-07-03T14:24:11Z
dc.date.issued2018-07-21
dc.date.submitted2017-09-29
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/277769
dc.description.abstractIn this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k>0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k<0$. We introduce a new representation, for the solution of the equation, as the optimal value of an optimal control problem. We also give a second representation which can be seen as a dual problem to the first optimisation problem. We note that this is a new type of dual problem and we compare it to the standard Lagrangian dual formulation. By choosing controls in the optimisation problems we obtain upper and lower bounds on the solution to the PDE. We use these bounds to study the speed of the wave front of the PDE in the case when $\mathcal{L}$ is the generator of a suitable Lévy process.
dc.description.sponsorshipResearch funded by EPSRC/CCA
dc.language.isoen
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectKPP
dc.subjectFKPP
dc.subjectReaction-Diffusion Equations
dc.subjectBranching processes
dc.subjectFront Propagation
dc.subjectHJB Equation
dc.subjectStochastic Optimisation
dc.subjectTravelling Waves
dc.titleAn Optimisation-Based Approach to FKPP-Type Equations
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentCambridge Centre for Analysis (CCA)
dc.date.updated2018-07-03T13:56:12Z
dc.identifier.doi10.17863/CAM.25108
dc.contributor.orcidDriver, David Philip [0000-0002-4159-8120]
dc.publisher.collegeChurchill College
dc.type.qualificationtitlePhD in Mathematics
cam.supervisorTehranchi, Michael
cam.thesis.fundingtrue
rioxxterms.freetoread.startdate2018-07-03


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