An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909215825592320 |
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| author | Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom |
| author_facet | Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom |
| contents | We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides both upper and lower bounds associated with the discrepancies in the drift, diffusion, and jump amplitude functions between the two jump-diffusion processes. Then, we propose a temporally decoupled squared $W_2$-distance method for efficiently reconstructing unknown jump-diffusion processes from data using parameterized neural networks. We further show its performance can be enhanced by utilizing prior information on the drift function of the jump-diffusion process. The effectiveness of our proposed reconstruction method is demonstrated across several examples and applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_01653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks Xia, Mingtao Li, Xiangting Shen, Qijing Chou, Tom Machine Learning Probability Applications Methodology 60G07, 60J76 We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides both upper and lower bounds associated with the discrepancies in the drift, diffusion, and jump amplitude functions between the two jump-diffusion processes. Then, we propose a temporally decoupled squared $W_2$-distance method for efficiently reconstructing unknown jump-diffusion processes from data using parameterized neural networks. We further show its performance can be enhanced by utilizing prior information on the drift function of the jump-diffusion process. The effectiveness of our proposed reconstruction method is demonstrated across several examples and applications. |
| title | An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks |
| topic | Machine Learning Probability Applications Methodology 60G07, 60J76 |
| url | https://arxiv.org/abs/2406.01653 |