Discussion Papers 2021
| CIRJE-F-1168 | "Deep Asymptotic Expansion with Weak Approximation" |
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| Author Name | Iguchi, Yuga, Riu Naito, Yusuke Okano, Akihiko Takahashi and Toshihiro Yamada |
| Date | May 2021 |
| Full Paper | |
| Remarks | Revised in August 2021. Published in 2021 IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE), March 2022. |
| Abstract |
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The paper proposes a new computational scheme for diffusion semigroups based on an asymptotic expansion with weak approximation and deep learning algorithm to solve high-dimensional Kolmogorov partial differential equations (PDEs). In particular, we give a spatial approximation for the solution of d-dimensional PDEs on a range [a; b]d without suffering from the curse of dimensionality. |
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Keywords. Deep learning, Asymptotic expansion, Weak approximation, Kolmogorov PDEs, Malliavin calculus, Curse of dimensionality |