Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths

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Abstract:This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural network-based estimator and derive a non-asymptotic convergence rate, decomposed into a training error, an approximation error, and a diffusion-related term scaling as ${\log N}/{N}$. For compositional drift functions, we establish an explicit rate. In the numerical experiments, we consider a drift function with local fluctuations generated by a double-layer compositional structure featuring local oscillations, and show that the empirical convergence rate becomes independent of the input dimension $d$. Compared to the $B$-spline method, the neural network estimator achieves better convergence rates and more effectively captures local features, particularly in higher-dimensional settings.

Comments: Accepted for an oral presentation at the 40th Annual AAAI Conference on Artificial Intelligence (AAAI-26)

Subjects:

Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST)

MSC classes: 62M45

Cite as: arXiv:2511.11161 [stat.ML]

(or arXiv:2511.11161v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2511.11161

arXiv-issued DOI via DataCite

Journal reference: Proceedings of the AAAI Conference on Artificial Intelligence, 2026, 40(34), 28778-28785

Related DOI:

https://doi.org/10.1609/aaai.v40i34.40111

DOI(s) linking to related resources

Submission history

From: Yuzhen Zhao [view email] [v1] Fri, 14 Nov 2025 10:56:52 UTC (673 KB) [v2] Tue, 31 Mar 2026 13:58:50 UTC (708 KB)