Existence of Lévy's area and pathwise integration
<p style="text-align:justify;"> Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which L´evy’s area plays a role. For vectors of irregular paths we investigate the relationship between the property of being controlled and...
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| Format: | Journal article |
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Louisiana State University Libraries
2015
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| _version_ | 1797077019246198784 |
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| author | Imkeller, P Prömel, D |
| author_facet | Imkeller, P Prömel, D |
| author_sort | Imkeller, P |
| collection | OXFORD |
| description | <p style="text-align:justify;"> Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which L´evy’s area plays a role. For vectors of irregular paths we investigate the relationship between the property of being controlled and the existence of associated L´evy areas. For two paths, one of which is controlled by the other, a pathwise construction of the L´evy area and therefore of mutual stochastic integrals is possible. If the existence of quadratic variation along a sequence of partitions is guaranteed, this leads us to a study of the pathwise change of variable (Itˆo) formula in the spirit of F¨ollmer, from the perspective of controlled paths. </p> |
| first_indexed | 2024-03-07T00:11:47Z |
| format | Journal article |
| id | oxford-uuid:797b54f1-8fc5-4b03-b0b0-1591822bf9c3 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:11:47Z |
| publishDate | 2015 |
| publisher | Louisiana State University Libraries |
| record_format | dspace |
| spelling | oxford-uuid:797b54f1-8fc5-4b03-b0b0-1591822bf9c32022-03-26T20:37:42ZExistence of Lévy's area and pathwise integrationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:797b54f1-8fc5-4b03-b0b0-1591822bf9c3Symplectic Elements at OxfordLouisiana State University Libraries2015Imkeller, PPrömel, D <p style="text-align:justify;"> Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which L´evy’s area plays a role. For vectors of irregular paths we investigate the relationship between the property of being controlled and the existence of associated L´evy areas. For two paths, one of which is controlled by the other, a pathwise construction of the L´evy area and therefore of mutual stochastic integrals is possible. If the existence of quadratic variation along a sequence of partitions is guaranteed, this leads us to a study of the pathwise change of variable (Itˆo) formula in the spirit of F¨ollmer, from the perspective of controlled paths. </p> |
| spellingShingle | Imkeller, P Prömel, D Existence of Lévy's area and pathwise integration |
| title | Existence of Lévy's area and pathwise integration |
| title_full | Existence of Lévy's area and pathwise integration |
| title_fullStr | Existence of Lévy's area and pathwise integration |
| title_full_unstemmed | Existence of Lévy's area and pathwise integration |
| title_short | Existence of Lévy's area and pathwise integration |
| title_sort | existence of levy s area and pathwise integration |
| work_keys_str_mv | AT imkellerp existenceoflevysareaandpathwiseintegration AT promeld existenceoflevysareaandpathwiseintegration |