Deep neural network approximation for high-dimensional parabolic partial integro-differential equations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913655952506880 |
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| author | Baranek, Marcin |
| author_facet | Baranek, Marcin |
| contents | In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we express the solution in terms of stochastic differential equations (SDEs). Based on several properties of classical estimators, we establish the existence of a DNN that satisfies the necessary assumptions. The results are theoretical and don't have any numerical experiments yet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep neural network approximation for high-dimensional parabolic partial integro-differential equations Baranek, Marcin Numerical Analysis In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we express the solution in terms of stochastic differential equations (SDEs). Based on several properties of classical estimators, we establish the existence of a DNN that satisfies the necessary assumptions. The results are theoretical and don't have any numerical experiments yet. |
| title | Deep neural network approximation for high-dimensional parabolic partial integro-differential equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.10880 |