An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
Abstract
We analyze the Wasserstein distance (-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared -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 -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.
Cite
@article{arxiv.2406.01653,
title = {An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks},
author = {Mingtao Xia and Xiangting Li and Qijing Shen and Tom Chou},
journal= {arXiv preprint arXiv:2406.01653},
year = {2024}
}