  We study the multiclass classification problem where the features come from
the mixture of time-homogeneous diffusions. 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 nonparametric estimators of the drift and diffusion
functions. We first establish the consistency of our classification procedure
under mild assumptions and then provide rates of cnvergence under different set
of assumptions. Finally, a numerical study supports our theoretical findings.
