  This article addresses the problem of functional supervised classification of
Cox process trajectories, whose random intensity is driven by some exogenous
random covariable. The classification task is achieved through a regularized
convex empirical risk minimization procedure, and a nonasymptotic oracle
inequality is derived. We show that the algorithm provides a Bayes-risk
consistent classifier. Furthermore, it is proved that the classifier converges
at a rate which adapts to the unknown regularity of the intensity process. Our
results are obtained by taking advantage of martingale and stochastic calculus
arguments, which are natural in this context and fully exploit the functional
nature of the problem.
