Rough path stability of (semi-)linear SPDEs
We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its Lévy area) as rough path noise the solution...
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| Format: | Journal article |
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Springer Verlag
2013
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| _version_ | 1797099250364973056 |
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| author | Friz, P Oberhauser, H |
| author_facet | Friz, P Oberhauser, H |
| author_sort | Friz, P |
| collection | OXFORD |
| description | We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its Lévy area) as rough path noise the solution coincides with the standard variational solution of the SPDE. |
| first_indexed | 2024-03-07T05:21:05Z |
| format | Journal article |
| id | oxford-uuid:deed4454-4554-4b6d-937f-538fd6b0890e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:21:05Z |
| publishDate | 2013 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:deed4454-4554-4b6d-937f-538fd6b0890e2022-03-27T09:35:40ZRough path stability of (semi-)linear SPDEsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:deed4454-4554-4b6d-937f-538fd6b0890eSymplectic Elements at OxfordSpringer Verlag2013Friz, POberhauser, HWe give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its Lévy area) as rough path noise the solution coincides with the standard variational solution of the SPDE. |
| spellingShingle | Friz, P Oberhauser, H Rough path stability of (semi-)linear SPDEs |
| title | Rough path stability of (semi-)linear SPDEs |
| title_full | Rough path stability of (semi-)linear SPDEs |
| title_fullStr | Rough path stability of (semi-)linear SPDEs |
| title_full_unstemmed | Rough path stability of (semi-)linear SPDEs |
| title_short | Rough path stability of (semi-)linear SPDEs |
| title_sort | rough path stability of semi linear spdes |
| work_keys_str_mv | AT frizp roughpathstabilityofsemilinearspdes AT oberhauserh roughpathstabilityofsemilinearspdes |