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arXiv 2602.17830stat.MLcs.LG
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具有去噪扩散模型的随机微分方程漂移估计

Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models

Marcos Tapia Costa, Nikolas Kantas, George Deligiannidis

AI总结:

本文提出利用去噪扩散模型估计随机微分方程中的漂移函数,该方法在不同维度下均表现出竞争力,且优势不受架构设计限制。

摘要:

我们研究了在已知扩散系数的情况下,从多个高频观测轨迹中估计多元随机微分方程中时间齐次漂移函数的问题。我们将漂移估计 formulation 为一个条件去噪问题,基于先前观测,提出了一种漂移函数估计器,该估计器是训练一个能够动态模拟新轨迹的条件扩散模型的副产品。在不同的漂移类别中,所提出的估计器在低维情况下与经典方法匹配,并在高维情况下保持一致的竞争力,其优势不能仅归因于架构设计选择。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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