CLASSIFICATION PROCEDURE FOR DIFFUSION PATHS

Recent advents in modern technology have generated labeled data recorded at high frequency,
that can be modelled as functional data. This work focuses on multiclass classification problem
for functional data modelled by a stochastic differential equation. Few works study the case where
functional data are modelled by diffusion processes, which is why the construction of classification
procedures adapted to this type of model is a major challenge. We focus on time-homogeneous
stochastic differential equations with unknown and non-parametric drift and diffusion coefficients.
The objective is to propose an implementable classification procedure based on the minimization
of the empirical risk of misclassification. For the resulting classification procedure to be imple-
mentable, we proceed to the convexfication of the model, replacing both the loss function and the
set of classifiers by convex surrogates. We then establish the consistency of the obtained empirical
classifier and derive some rates of convergence over the Hölder space. The theoretical study is
completed with a numerical illustration over simulated data