We study the multiclass classification problem where the features come from a mixture of time-homogeneous diffusion.Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown.In this framework, we build a plug-in classifier which relies on nonparamateric estimators of the drift and diffusion functions.We first establish the consistency of our classification procedure under mild assumptions and then provide rates of convergence under different setof assumptions. Finally, a numerical study supports our theoretical findings.

中文翻译：

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用于 SDE 路径多类分类的非参数插件分类器

我们研究多类分类问题，其中特征来自时间同质扩散的混合。具体来说，类通过它们的漂移函数来区分，而扩散系数对于所有类来说是公共的且未知。在这个框架中，我们构建了一个插件在依赖于漂移和扩散函数的非参数估计量的分类器中。我们首先在温和的假设下建立分类过程的一致性，然后提供不同假设下的收敛率。最后，数值研究支持了我们的理论发现。