{"ID":2827495,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.16396","arxiv_id":"2512.16396","title":"Global universal approximation with Brownian signatures","abstract":"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.","short_abstract":"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 theore...","url_abs":"https://arxiv.org/abs/2512.16396","url_pdf":"https://arxiv.org/pdf/2512.16396v1","authors":"[\"Mihriban Ceylan\",\"David J. Prömel\"]","published":"2025-12-18T10:49:20Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"cs.LG\",\"q-fin.MF\"]","methods":"[]","has_code":false}