Path-dependent processes from signatures
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911247146942464 |
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| author | Jaber, Eduardo Abi Gérard, Louis-Amand Huang, Yuxing |
| author_facet | Jaber, Eduardo Abi Gérard, Louis-Amand Huang, Yuxing |
| contents | We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear Volterra and delay equations and in particular the fractional Brownian motion with a Hurst index $H \in (0, 1)$. Our expressions allow to disentangle an infinite dimensional Markovian structure and open the door to straightforward and simple approximation schemes, that we illustrate numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Path-dependent processes from signatures Jaber, Eduardo Abi Gérard, Louis-Amand Huang, Yuxing Probability 60L10, 60L70, 60H20, 60G22 We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear Volterra and delay equations and in particular the fractional Brownian motion with a Hurst index $H \in (0, 1)$. Our expressions allow to disentangle an infinite dimensional Markovian structure and open the door to straightforward and simple approximation schemes, that we illustrate numerically. |
| title | Path-dependent processes from signatures |
| topic | Probability 60L10, 60L70, 60H20, 60G22 |
| url | https://arxiv.org/abs/2407.04956 |