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

• URL: http://arxiv.org/abs/2511.11161v1
• Date: Fri, 14 Nov 2025 10:56:52 GMT
• Title: Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths
• Authors: Yuzhen Zhao, Yating Liu, Marc Hoffmann,
• Abstract summary: This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process.<n>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 $log N/N$.
• Score: 10.214978140001858
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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