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Dynamical large deviations of diffusions
Thesis (PhD)--Stellenbosch University, 2023.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2023
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| _version_ | 1867614115827023872 |
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| access_status_str | Open Access |
| author | Du Buisson, Johannes Petrus |
| author2 | Touchette, Hugo |
| author_browse | Du Buisson, Johannes Petrus Touchette, Hugo |
| author_facet | Touchette, Hugo Du Buisson, Johannes Petrus |
| author_sort | Du Buisson, Johannes Petrus |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2023. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/126966 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:55.034Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/126966 Dynamical large deviations of diffusions Du Buisson, Johannes Petrus Touchette, Hugo Muller-Nedebock, Kristian K. Stellenbosch University. Faculty of Science. Dept. of Physics. Large deviations -- Mathematical models Diffusion processes Markov processes -- Numerical solutions Stochastic differential equations -- Mathematical models UCTD Thesis (PhD)--Stellenbosch University, 2023. ENGLISH ABSTRACT: We solve two problems related to the fluctuations o f t ime-integrated function- als of Markov diffusions, u sed i n p hysics t o m odel n onequilibrium s ystems. In the first w e d erive a nd i llustrate t he a ppropriate b oundary c onditions o n the spectral problem used to obtain the large deviations of current-type observables for reflected d iffusions. Fo r th e se cond pr oblem we st udy li near di ffusions and obtain exact results for the generating function associated with linear additive, quadratic additive and linear current-type observables by using the Feynman- Kac formula. We investigate the long-time behavior of the generating function for each of these observables to determine both the so-called rate function and the form of the effective p rocess r esponsible f or m anifesting t he fl uctuations of the associated observable. It is found that for each of these observables, the effective p rocess i s a gain a l inear d iffusion. We ap ply ou r ge neral re sults fo r a variety of linear diffusions i n R ², w ith p articular e mphasis o n i nvestigating the manner in which the density and current of the original process are modified in order to create fluctuations. AFRIKAANSE OPSOMMING: Ons los twee probleme op wat verband hou met die fluktuasies van tyd-geïntegreerde funksionale van Markov-diffusies, wat in fisika gebruik word om sisteme buite termiese ewewig te modelleer. Vir die eerste probleem lei ons die toepaslike randvoorwaardes af vir die spektrale probleem wat gebruik word om die groot afwykings van stroom-tipe waarneembares van gereflekteerde diffusies te bekom en illustreer ook ons resultate. Vir die tweede probleem bestudeer ons lineêre diffusies en verkry eksakte resultate vir die genererende funksie wat met lineêre digtheids-, kwadratiese digtheids- en lineêre stroom-tipe waarneembares geasso- sieer word deur van die Feynman-Kac formule gebruik te maak. Ons ondersoek die groot-tyd gedrag van die genererende funskie vir elk van hierdie waarneem- bares en verkry die sogenoemde tempo-funksie asook die vorm van die effektiewe proses wat verantwoordelik is vir die manifestering van fluktuasies van die geas- sosieerde waarneembare. Dit word bevind dat vir elk van hierdie waarneembares is die effektiewe proses weereens ’n lineêre diffusie. Ons pas ons algemene re- sultate toe vir ’n verskeidenheid lineêre diffusies in R², met spesifieke klem op die ondersoek van die wyse waarop die digtheid en stroom van die oorspronklike proses aangepas word in orde om fluksuasies te skep. Doctoral 2023-01-31T16:24:19Z 2023-05-18T06:57:57Z 2023-01-31T16:24:19Z 2023-05-18T06:57:57Z 2023-03 Thesis http://hdl.handle.net/10019.1/126966 en_ZA Stellenbosch University ix, 110 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Large deviations -- Mathematical models Diffusion processes Markov processes -- Numerical solutions Stochastic differential equations -- Mathematical models UCTD Du Buisson, Johannes Petrus Dynamical large deviations of diffusions |
| title | Dynamical large deviations of diffusions |
| title_full | Dynamical large deviations of diffusions |
| title_fullStr | Dynamical large deviations of diffusions |
| title_full_unstemmed | Dynamical large deviations of diffusions |
| title_short | Dynamical large deviations of diffusions |
| title_sort | dynamical large deviations of diffusions |
| topic | Large deviations -- Mathematical models Diffusion processes Markov processes -- Numerical solutions Stochastic differential equations -- Mathematical models UCTD |
| url | http://hdl.handle.net/10019.1/126966 |
| work_keys_str_mv | AT dubuissonjohannespetrus dynamicallargedeviationsofdiffusions |