VARIETIES OF SIGNATURE TENSORS
The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is examined here through the lens of algebraic geometry. We introduce varieties of signature tensors for both determ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2019-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000033/type/journal_article |
| _version_ | 1811156175983476736 |
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| author | CARLOS AMÉNDOLA PETER FRIZ BERND STURMFELS |
| author_facet | CARLOS AMÉNDOLA PETER FRIZ BERND STURMFELS |
| author_sort | CARLOS AMÉNDOLA |
| collection | DOAJ |
| description | The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is examined here through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures. |
| first_indexed | 2024-04-10T04:47:09Z |
| format | Article |
| id | doaj.art-5da2212b737241909d1d906818580c34 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:09Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-5da2212b737241909d1d906818580c342023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.3VARIETIES OF SIGNATURE TENSORSCARLOS AMÉNDOLA0PETER FRIZ1BERND STURMFELS2Technische Universität München, Germany;Technische Universität Berlin and WIAS Berlin, Germany;MPI for Mathematics in the Sciences, Leipzig and UC Berkeley, Germany;The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is examined here through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures.https://www.cambridge.org/core/product/identifier/S2050509419000033/type/journal_article14Q1560H99 |
| spellingShingle | CARLOS AMÉNDOLA PETER FRIZ BERND STURMFELS VARIETIES OF SIGNATURE TENSORS Forum of Mathematics, Sigma 14Q15 60H99 |
| title | VARIETIES OF SIGNATURE TENSORS |
| title_full | VARIETIES OF SIGNATURE TENSORS |
| title_fullStr | VARIETIES OF SIGNATURE TENSORS |
| title_full_unstemmed | VARIETIES OF SIGNATURE TENSORS |
| title_short | VARIETIES OF SIGNATURE TENSORS |
| title_sort | varieties of signature tensors |
| topic | 14Q15 60H99 |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000033/type/journal_article |
| work_keys_str_mv | AT carlosamendola varietiesofsignaturetensors AT peterfriz varietiesofsignaturetensors AT berndsturmfels varietiesofsignaturetensors |