Alberti's type rank one theorem for martingales
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909444817813504 |
|---|---|
| author | Ayoush, Rami Stolyarov, Dmitriy Wojciechowski, Michał |
| author_facet | Ayoush, Rami Stolyarov, Dmitriy Wojciechowski, Michał |
| contents | We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the $q$-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti's rank-one theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11381 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Alberti's type rank one theorem for martingales Ayoush, Rami Stolyarov, Dmitriy Wojciechowski, Michał Functional Analysis Probability We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the $q$-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti's rank-one theorem. |
| title | Alberti's type rank one theorem for martingales |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2307.11381 |