Non-Linear diffusion processes and applications

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dc.contributor.advisorVarughese, Melvinen_ZA
dc.contributor.authorPienaar, Etienne A Den_ZA
dc.date.accessioned2017-01-24T09:09:07Z
dc.date.available2017-01-24T09:09:07Z
dc.date.issued2016en_ZA
dc.description.abstractDiffusion models are useful tools for quantifying the dynamics of continuously evolving processes. Using diffusion models it is possible to formulate compact descriptions for the dynamics of real-world processes in terms of stochastic differential equations. Despite the exibility of these models, they can often be extremely difficult to work with. This is especially true for non-linear and/or time-inhomogeneous diffusion models where even basic statistical properties of the process can be elusive. As such, we explore various techniques for analysing non-linear diffusion models in contexts ranging from conducting inference under discrete observation and solving first passage time problems, to the analysis of jump diffusion processes and highly non-linear diffusion processes. We apply the methodology to a number of real-world ecological and financial problems of interest and demonstrate how non-linear diffusion models can be used to better understand such phenomena. In conjunction with the methodology, we develop a series of software packages that can be used to accurately and efficiently analyse various classes of non-linear diffusion models.en_ZA
dc.identifier.apacitationPienaar, E. A. D. (2016). <i>Non-Linear diffusion processes and applications</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/22973en_ZA
dc.identifier.chicagocitationPienaar, Etienne A D. <i>"Non-Linear diffusion processes and applications."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2016. http://hdl.handle.net/11427/22973en_ZA
dc.identifier.citationPienaar, E. 2016. Non-Linear diffusion processes and applications. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Pienaar, Etienne A D AB - Diffusion models are useful tools for quantifying the dynamics of continuously evolving processes. Using diffusion models it is possible to formulate compact descriptions for the dynamics of real-world processes in terms of stochastic differential equations. Despite the exibility of these models, they can often be extremely difficult to work with. This is especially true for non-linear and/or time-inhomogeneous diffusion models where even basic statistical properties of the process can be elusive. As such, we explore various techniques for analysing non-linear diffusion models in contexts ranging from conducting inference under discrete observation and solving first passage time problems, to the analysis of jump diffusion processes and highly non-linear diffusion processes. We apply the methodology to a number of real-world ecological and financial problems of interest and demonstrate how non-linear diffusion models can be used to better understand such phenomena. In conjunction with the methodology, we develop a series of software packages that can be used to accurately and efficiently analyse various classes of non-linear diffusion models. DA - 2016 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2016 T1 - Non-Linear diffusion processes and applications TI - Non-Linear diffusion processes and applications UR - http://hdl.handle.net/11427/22973 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22973
dc.identifier.vancouvercitationPienaar EAD. Non-Linear diffusion processes and applications. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2016 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22973en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherStatisticsen_ZA
dc.titleNon-Linear diffusion processes and applicationsen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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