{"ID":2841640,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11161","arxiv_id":"2511.11161","title":"Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths","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.","short_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 in...","url_abs":"https://arxiv.org/abs/2511.11161","url_pdf":"https://arxiv.org/pdf/2511.11161v2","authors":"[\"Yuzhen Zhao\",\"Yating Liu\",\"Marc Hoffmann\"]","published":"2025-11-14T10:56:52Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.ST\"]","methods":"[\"Diffusion Model\"]","has_code":false}