Rough path limits of the Wong–Zakai type with a modified drift term
The Wong-Zakai theorem asserts that ODEs driven by "reasonable" (e.g. piecewise linear) approximations of Brownian motion converge to the corresponding Stratonovich stochastic differential equation. With the aid of rough path analysis, we study "non-reasonable" approximations and...
| Κύριοι συγγραφείς: | , |
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| Μορφή: | Journal article |
| Γλώσσα: | English |
| Έκδοση: |
Elsevier
2009
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| _version_ | 1826312362852876288 |
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| author | Friz, P Oberhauser, H |
| author_facet | Friz, P Oberhauser, H |
| author_sort | Friz, P |
| collection | OXFORD |
| description | The Wong-Zakai theorem asserts that ODEs driven by "reasonable" (e.g. piecewise linear) approximations of Brownian motion converge to the corresponding Stratonovich stochastic differential equation. With the aid of rough path analysis, we study "non-reasonable" approximations and go beyond a well-known criterion of [Ikeda, Watanabe, North Holland, 1989] in the sense that our result applies to perturbations on all levels, exhibiting additional drift terms involving any iterated Lie brackets of the driving vector fields. In particular, this applies to the approximations by McShane ('72) and Sussmann ('91). Our approach is not restricted to Brownian driving signals. At last, these ideas can be used to prove optimality of certain rough path estimates. |
| first_indexed | 2024-03-07T08:26:27Z |
| format | Journal article |
| id | oxford-uuid:932b6f74-3ae9-48b7-a6e9-2d48f91bcf2d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:26:27Z |
| publishDate | 2009 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:932b6f74-3ae9-48b7-a6e9-2d48f91bcf2d2024-02-20T16:38:11ZRough path limits of the Wong–Zakai type with a modified drift termJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:932b6f74-3ae9-48b7-a6e9-2d48f91bcf2dEnglishSymplectic Elements at OxfordElsevier2009Friz, POberhauser, HThe Wong-Zakai theorem asserts that ODEs driven by "reasonable" (e.g. piecewise linear) approximations of Brownian motion converge to the corresponding Stratonovich stochastic differential equation. With the aid of rough path analysis, we study "non-reasonable" approximations and go beyond a well-known criterion of [Ikeda, Watanabe, North Holland, 1989] in the sense that our result applies to perturbations on all levels, exhibiting additional drift terms involving any iterated Lie brackets of the driving vector fields. In particular, this applies to the approximations by McShane ('72) and Sussmann ('91). Our approach is not restricted to Brownian driving signals. At last, these ideas can be used to prove optimality of certain rough path estimates. |
| spellingShingle | Friz, P Oberhauser, H Rough path limits of the Wong–Zakai type with a modified drift term |
| title | Rough path limits of the Wong–Zakai type with a modified drift term |
| title_full | Rough path limits of the Wong–Zakai type with a modified drift term |
| title_fullStr | Rough path limits of the Wong–Zakai type with a modified drift term |
| title_full_unstemmed | Rough path limits of the Wong–Zakai type with a modified drift term |
| title_short | Rough path limits of the Wong–Zakai type with a modified drift term |
| title_sort | rough path limits of the wong zakai type with a modified drift term |
| work_keys_str_mv | AT frizp roughpathlimitsofthewongzakaitypewithamodifieddriftterm AT oberhauserh roughpathlimitsofthewongzakaitypewithamodifieddriftterm |