Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929383440121856 |
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| author | Neufeld, Ariel Nguyen, Tuan Anh |
| author_facet | Neufeld, Ariel Nguyen, Tuan Anh |
| contents | In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean--Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension $d$ of the SDE and the reciprocal of the accuracy $ε$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07042 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations Neufeld, Ariel Nguyen, Tuan Anh Numerical Analysis Probability In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean--Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension $d$ of the SDE and the reciprocal of the accuracy $ε$. |
| title | Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2312.07042 |