We study a supervised multiclass classification problem for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. Extending the one-dimensional multiclass framework of Denis et al. (2024) to multidimensional diffusions, we propose a neural network-based plug-in classifier that estimates the drift functions for each class from independent sample paths and assigns labels based on a Bayes-type decision rule. Under standard regularity assumptions, we establish convergence rates for the excess misclassification risk, explicitly capturing the effects of drift estimation error and time discretization. Numerical experiments demonstrate that the proposed method achieves faster convergence and improved classification performance compared to Denis et al. (2024) in the one-dimensional setting, remains effective in higher dimensions when the underlying drift functions admit a compositional structure, and consistently outperforms direct neural network classifiers trained end-to-end on trajectories without exploiting the diffusion model structure.

翻译：本文研究扩散过程的监督多分类问题，其中每个类别由不同的漂移函数表征，且轨迹在离散时间点被观测。我们将Denis等人（2024）的一维多分类框架扩展至多维扩散过程，提出一种基于神经网络的插件式分类器：该分类器从独立样本路径中估计各类别的漂移函数，并依据贝叶斯型决策规则进行标签分配。在标准正则性假设下，我们建立了超额误分类风险的收敛速率，明确刻画了漂移估计误差与时间离散化的影响。数值实验表明：在一维场景中，所提方法相比Denis等人（2024）获得了更快的收敛速度与更优的分类性能；当底层漂移函数具有复合结构时，该方法在高维场景中仍保持有效性；且相较于未利用扩散模型结构、直接对轨迹进行端到端训练的神经网络分类器，本方法始终表现出更优越的性能。