{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/22973"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/22973","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Non-Linear diffusion processes and applications","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Pienaar, Etienne A D"],"institution":"Department of Statistical Sciences","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Varughese, Melvin"],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-22T22:22:57Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/22973","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Varughese, Melvin"]},{"key":"dc:creator","label":"Author","values":["Pienaar, Etienne A D"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-01-24T09:09:07Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-01-24T09:09:07Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Statistical Sciences"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/22973"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Non-Linear diffusion processes and applications"]}]}],"canonical_facts":{"dc:contributor.advisor":["Varughese, Melvin"],"dc:creator":["Pienaar, Etienne A D"],"dc:date.accessioned":["2017-01-24T09:09:07Z"],"dc:date.available":["2017-01-24T09:09:07Z"],"dc:date.issued":["2016"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/22973"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Statistical Sciences"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Non-Linear diffusion processes and applications"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:22:57Z"}