On pathwise quadratic variation for càdlàg functions
We revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
Institute of Mathematical Statistics
2018
|
| _version_ | 1826288451788472320 |
|---|---|
| author | Chiu, H Cont, R |
| author_facet | Chiu, H Cont, R |
| author_sort | Chiu, H |
| collection | OXFORD |
| description | We revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition which implies the Lebesgue decomposition of the pathwise quadratic variation as a result, rather than requiring it as an extra condition. |
| first_indexed | 2024-03-07T02:13:54Z |
| format | Journal article |
| id | oxford-uuid:a191f291-8ff6-42fc-8e26-bdd0e89dc90a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:13:54Z |
| publishDate | 2018 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:a191f291-8ff6-42fc-8e26-bdd0e89dc90a2022-03-27T02:14:08ZOn pathwise quadratic variation for càdlàg functionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a191f291-8ff6-42fc-8e26-bdd0e89dc90aSymplectic Elements at OxfordInstitute of Mathematical Statistics2018Chiu, HCont, RWe revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition which implies the Lebesgue decomposition of the pathwise quadratic variation as a result, rather than requiring it as an extra condition. |
| spellingShingle | Chiu, H Cont, R On pathwise quadratic variation for càdlàg functions |
| title | On pathwise quadratic variation for càdlàg functions |
| title_full | On pathwise quadratic variation for càdlàg functions |
| title_fullStr | On pathwise quadratic variation for càdlàg functions |
| title_full_unstemmed | On pathwise quadratic variation for càdlàg functions |
| title_short | On pathwise quadratic variation for càdlàg functions |
| title_sort | on pathwise quadratic variation for cadlag functions |
| work_keys_str_mv | AT chiuh onpathwisequadraticvariationforcadlagfunctions AT contr onpathwisequadraticvariationforcadlagfunctions |