An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
<|reference_start|>An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks: 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.<|reference_end|>
@article{xia2024an,
    title={An efficient Wasserstein-distance approach for reconstructing
  jump-diffusion processes using parameterized neural networks},
    author={Mingtao Xia, Xiangting Li, Qijing Shen, Tom Chou},
    journal={arXiv preprint arXiv:2406.01653},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.01653},
    primaryClass={stat.ML cs.LG math.PR stat.AP stat.ME}
}