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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.14884 |
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| _version_ | 1866915183547383808 |
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| author | Vogler, Alexander Stannat, Wilhelm |
| author_facet | Vogler, Alexander Stannat, Wilhelm |
| contents | In this paper we present a new interpretation of the Lions derivative as the Radon-Nikodym derivative of a vector measure, which provides a canonical extension of the Lions derivative for functions taking values in infinite dimensional Banach spaces. This is of particular relevance for the analysis of Hilbert space valued Mean-Field equations. As an illustration we derive a mild Ito-formula for Mean-Field stochastic partial differential equations (SPDEs), which provides the basis for a higher order Taylor expansion and higher order numerical schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Lions Derivative in Infinite Dimensions -- Application to Higher Order Expansion of Mean-Field SPDEs Vogler, Alexander Stannat, Wilhelm Probability In this paper we present a new interpretation of the Lions derivative as the Radon-Nikodym derivative of a vector measure, which provides a canonical extension of the Lions derivative for functions taking values in infinite dimensional Banach spaces. This is of particular relevance for the analysis of Hilbert space valued Mean-Field equations. As an illustration we derive a mild Ito-formula for Mean-Field stochastic partial differential equations (SPDEs), which provides the basis for a higher order Taylor expansion and higher order numerical schemes. |
| title | The Lions Derivative in Infinite Dimensions -- Application to Higher Order Expansion of Mean-Field SPDEs |
| topic | Probability |
| url | https://arxiv.org/abs/2407.14884 |