Global universal approximation with Brownian signatures
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909968724131840 |
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| author | Ceylan, Mihriban Prömel, David J. |
| author_facet | Ceylan, Mihriban Prömel, David J. |
| contents | We establish $L^p$-type universal approximation theorems for general and non-anticipative functionals on suitable rough path spaces, showing that linear functionals acting on signatures of time-extended rough paths are dense with respect to an $L^p$-distance. To that end, we derive global universal approximation theorems for weighted rough path spaces. We demonstrate that these $L^p$-type universal approximation theorems apply in particular to Brownian motion. As a consequence, linear functionals on the signature of the time-extended Brownian motion can approximate any $p$-integrable stochastic process adapted to the Brownian filtration, including solutions to stochastic differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global universal approximation with Brownian signatures Ceylan, Mihriban Prömel, David J. Probability Machine Learning Mathematical Finance We establish $L^p$-type universal approximation theorems for general and non-anticipative functionals on suitable rough path spaces, showing that linear functionals acting on signatures of time-extended rough paths are dense with respect to an $L^p$-distance. To that end, we derive global universal approximation theorems for weighted rough path spaces. We demonstrate that these $L^p$-type universal approximation theorems apply in particular to Brownian motion. As a consequence, linear functionals on the signature of the time-extended Brownian motion can approximate any $p$-integrable stochastic process adapted to the Brownian filtration, including solutions to stochastic differential equations. |
| title | Global universal approximation with Brownian signatures |
| topic | Probability Machine Learning Mathematical Finance |
| url | https://arxiv.org/abs/2512.16396 |