Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915975009402880 |
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| author | Dause, Jannis R. Friz, Peter K. Jentzen, Arnulf Song, Jian |
| author_facet | Dause, Jannis R. Friz, Peter K. Jentzen, Arnulf Song, Jian |
| contents | We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semimartingales and yields a rough stochastic Itô-Wentzell formula under natural and verifiable regularity assumptions. Our motivation comes from works of Hudde et al. (2024) and, independently, Del Moral and Singh (2022) where the authors established, respectively, Itô-Alekseev-Gröbner, backward Itô-Wentzell, and diffusion interpolation formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities Dause, Jannis R. Friz, Peter K. Jentzen, Arnulf Song, Jian Probability 60H05 (Primary) 60L20, 60H10, 60H07, 60J60, 65C30, 65C20 (Secondary) We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semimartingales and yields a rough stochastic Itô-Wentzell formula under natural and verifiable regularity assumptions. Our motivation comes from works of Hudde et al. (2024) and, independently, Del Moral and Singh (2022) where the authors established, respectively, Itô-Alekseev-Gröbner, backward Itô-Wentzell, and diffusion interpolation formulas. |
| title | Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities |
| topic | Probability 60H05 (Primary) 60L20, 60H10, 60H07, 60J60, 65C30, 65C20 (Secondary) |
| url | https://arxiv.org/abs/2603.05388 |