On local times, density estimation and supervised classification from functional data

In this paper, we define a n-consistent nonparametric estimator for the marginal density function of an order one stationary process built up from a sample of i.i.d continuous time trajectories. Under mild conditions we obtain strong consistency, strong orders of convergence and derive the asymptotic distribution of the estimator. We extend some of the results to the non-stationary case. We propose a nonparametric classification rule based on local times (occupation measure) and include some simulations studies.