We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate drift estimation as a denoising problem conditional on previous observations, and propose an estimator of the drift function which is a by-product of training a conditional diffusion model capable of simulating new trajectories dynamically. Across different drift classes, the proposed estimator was found to match classical methods in low dimensions and remained consistently competitive in higher dimensions, with gains that cannot be attributed to architectural design choices alone.

翻译：本文研究多元随机微分方程中时间齐次漂移函数的估计问题，其中扩散系数已知，且观测数据为固定时间范围内高频采样的多条轨迹。我们将漂移估计构建为基于历史观测的条件去噪问题，并提出一种漂移函数估计器，该估计器作为训练条件扩散模型的副产品获得，该模型能够动态模拟新轨迹。在不同漂移函数类别中，所提估计器在低维情况下与经典方法性能相当，在高维情况下始终保持竞争力，其优势不能仅归因于网络架构设计选择。