An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks

2024/06/03 by Mingtao Xia, Xia, Mingtao, Xiangting Li +5 · 1 citation
Medicine · Physics and Astronomy · #60G07 #60J76 #Advanced Neuroimaging Techniques and Applications #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Model Reduction and Neural Networks #NMR spectroscopy and applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2406.01653

openalex publication_date 2024/06/03 · openalex created_date 2024/07/31 · openalex updated_date 2026/07/28

Abstract

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 W₂-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 W₂-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.

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