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Non-Linear diffusion processes and applications
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, th...
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| Format: | Thesis |
| Language: | English |
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Department of Statistical Sciences
2017
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| _version_ | 1867613217949220864 |
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| access_status_str | Open Access |
| author | Pienaar, Etienne A D |
| author2 | Varughese, Melvin |
| author_browse | Pienaar, Etienne A D Varughese, Melvin |
| author_facet | Varughese, Melvin Pienaar, Etienne A D |
| author_sort | Pienaar, Etienne A D |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22973 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:38.580Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Department of Statistical Sciences |
| publisherStr | Department of Statistical Sciences |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/22973 Non-Linear diffusion processes and applications Pienaar, Etienne A D Varughese, Melvin Statistics 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. 2017-01-24T09:09:07Z 2017-01-24T09:09:07Z 2016 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/22973 eng application/pdf Department of Statistical Sciences Faculty of Science University of Cape Town |
| spellingShingle | Statistics Pienaar, Etienne A D Non-Linear diffusion processes and applications |
| thesis_degree_str | Doctoral |
| title | Non-Linear diffusion processes and applications |
| title_full | Non-Linear diffusion processes and applications |
| title_fullStr | Non-Linear diffusion processes and applications |
| title_full_unstemmed | Non-Linear diffusion processes and applications |
| title_short | Non-Linear diffusion processes and applications |
| title_sort | non linear diffusion processes and applications |
| topic | Statistics |
| url | http://hdl.handle.net/11427/22973 |
| work_keys_str_mv | AT pienaaretiennead nonlineardiffusionprocessesandapplications |