Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian
<p>This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function on this space. The second associates an expected signature to the bilaplacian and culminates in an analogue of the Feynman-Kac formula for...
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| Format: | Thesis |
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2018
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| _version_ | 1826273568466403328 |
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| author | Nejad, S |
| author2 | Lyons, T |
| author_facet | Lyons, T Nejad, S |
| author_sort | Nejad, S |
| collection | OXFORD |
| description | <p>This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function on this space. The second associates an expected signature to the bilaplacian and culminates in an analogue of the Feynman-Kac formula for high-order parabolic partial differential equations.</p> |
| first_indexed | 2024-03-06T22:30:11Z |
| format | Thesis |
| id | oxford-uuid:5805be09-93e5-4f18-b960-732f81f85860 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:30:11Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oxford-uuid:5805be09-93e5-4f18-b960-732f81f858602022-03-26T17:00:24ZLipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacianThesishttp://purl.org/coar/resource_type/c_db06uuid:5805be09-93e5-4f18-b960-732f81f85860Stochastic analysisRough pathsORA Deposit2018Nejad, SLyons, T<p>This thesis is a tale of two halves. The first introduces the space of unparameterised geometric rough paths and develops a notion of Lipschitz function on this space. The second associates an expected signature to the bilaplacian and culminates in an analogue of the Feynman-Kac formula for high-order parabolic partial differential equations.</p> |
| spellingShingle | Stochastic analysis Rough paths Nejad, S Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title | Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title_full | Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title_fullStr | Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title_full_unstemmed | Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title_short | Lipschitz functions on unparameterised rough paths and the Brownian motion associated to the bilaplacian |
| title_sort | lipschitz functions on unparameterised rough paths and the brownian motion associated to the bilaplacian |
| topic | Stochastic analysis Rough paths |
| work_keys_str_mv | AT nejads lipschitzfunctionsonunparameterisedroughpathsandthebrownianmotionassociatedtothebilaplacian |