Global universality via discrete-time signatures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910048062537728 |
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| author | Ceylan, Mihriban Prömel, David J. |
| author_facet | Ceylan, Mihriban Prömel, David J. |
| contents | We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition on the underlying weight function. As an application, we show that piecewise linear interpolations of Brownian motion satisfies this integrability condition. Consequently, we obtain $L^p$-approximation results for path-dependent functionals, random ordinary differential equations, and stochastic differential equations driven by Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global universality via discrete-time signatures Ceylan, Mihriban Prömel, David J. Probability Machine Learning Mathematical Finance We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition on the underlying weight function. As an application, we show that piecewise linear interpolations of Brownian motion satisfies this integrability condition. Consequently, we obtain $L^p$-approximation results for path-dependent functionals, random ordinary differential equations, and stochastic differential equations driven by Brownian motion. |
| title | Global universality via discrete-time signatures |
| topic | Probability Machine Learning Mathematical Finance |
| url | https://arxiv.org/abs/2603.09773 |