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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17437 |
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| _version_ | 1866910027136106496 |
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| author | Bruned, Yvain Hou, Yingtong Laubie, Paul Zhu, Zhicheng |
| author_facet | Bruned, Yvain Hou, Yingtong Laubie, Paul Zhu, Zhicheng |
| contents | In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Bailleul flow approach. This assumption requires that the rough path associated with the equation is given by a Hopf algebra whose coproduct admits a cocycle and has a tree-like basis. We show that the Hopf algebra of multi-indices does not satisfy the cocycle condition. This is a rigorous result on the impossibility, observed in practice, of performing a fixed point argument for multi-indices rough paths and multi-indices in Regularity Structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Banach fixed point and flow approach for rough analysis Bruned, Yvain Hou, Yingtong Laubie, Paul Zhu, Zhicheng Probability Analysis of PDEs Rings and Algebras In this paper, we show that the main algebraic assumption required to perform a fixed point argument for rough differential equations implies the algebraic assumption for the Bailleul flow approach. This assumption requires that the rough path associated with the equation is given by a Hopf algebra whose coproduct admits a cocycle and has a tree-like basis. We show that the Hopf algebra of multi-indices does not satisfy the cocycle condition. This is a rigorous result on the impossibility, observed in practice, of performing a fixed point argument for multi-indices rough paths and multi-indices in Regularity Structures. |
| title | Banach fixed point and flow approach for rough analysis |
| topic | Probability Analysis of PDEs Rings and Algebras |
| url | https://arxiv.org/abs/2602.17437 |