Stochastic PDEs and weakly interacting particle systems
<p>We study two problems relating to weakly interacting particle systems in the presence of exogenous noise. Part I presents a pathwise regularisation by noise result for McKean–Vlasov equations with singular interaction kernels. Using ideas from the theory of averaged fields and non-linear Yo...
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| Format: | Thesis |
| Language: | English |
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2020
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| _version_ | 1826277707683463168 |
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| author | Mayorcas, A |
| author2 | Hambly, B |
| author_facet | Hambly, B Mayorcas, A |
| author_sort | Mayorcas, A |
| collection | OXFORD |
| description | <p>We study two problems relating to weakly interacting particle systems in the presence of exogenous noise. Part I presents a pathwise regularisation by noise result for McKean–Vlasov equations with singular interaction kernels. Using ideas from the theory of averaged fields and non-linear Young integrals we obtain well-posedness of the McKean–Vlasov systems, particle approximations and mean field convergence.</p>
<p>In Part II we study a family of semi-linear, convection-diffusion SPDEs that are closely related to PDEs coming from the theory of collision-less kinetics. We study these equations in the presence of additive spacetime white noise. In one dimension we show global well-posedness and exponential ergodicity for an equation with a cubic non-linearity and repulsive sign choice. In two dimensions we show local well-posedness for a renormalised equation.</p> |
| first_indexed | 2024-03-06T23:32:58Z |
| format | Thesis |
| id | oxford-uuid:6cb19c41-0598-4b23-bcb6-bf91ce44c727 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:32:58Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:6cb19c41-0598-4b23-bcb6-bf91ce44c7272022-03-26T19:12:41ZStochastic PDEs and weakly interacting particle systemsThesishttp://purl.org/coar/resource_type/c_db06uuid:6cb19c41-0598-4b23-bcb6-bf91ce44c727Stochastic partial differential equationsMathematicsStochastic analysisEnglishHyrax Deposit2020Mayorcas, AHambly, BChevyrev, IWeber, HQian, Z<p>We study two problems relating to weakly interacting particle systems in the presence of exogenous noise. Part I presents a pathwise regularisation by noise result for McKean–Vlasov equations with singular interaction kernels. Using ideas from the theory of averaged fields and non-linear Young integrals we obtain well-posedness of the McKean–Vlasov systems, particle approximations and mean field convergence.</p> <p>In Part II we study a family of semi-linear, convection-diffusion SPDEs that are closely related to PDEs coming from the theory of collision-less kinetics. We study these equations in the presence of additive spacetime white noise. In one dimension we show global well-posedness and exponential ergodicity for an equation with a cubic non-linearity and repulsive sign choice. In two dimensions we show local well-posedness for a renormalised equation.</p> |
| spellingShingle | Stochastic partial differential equations Mathematics Stochastic analysis Mayorcas, A Stochastic PDEs and weakly interacting particle systems |
| title | Stochastic PDEs and weakly interacting particle systems |
| title_full | Stochastic PDEs and weakly interacting particle systems |
| title_fullStr | Stochastic PDEs and weakly interacting particle systems |
| title_full_unstemmed | Stochastic PDEs and weakly interacting particle systems |
| title_short | Stochastic PDEs and weakly interacting particle systems |
| title_sort | stochastic pdes and weakly interacting particle systems |
| topic | Stochastic partial differential equations Mathematics Stochastic analysis |
| work_keys_str_mv | AT mayorcasa stochasticpdesandweaklyinteractingparticlesystems |