Abstract
The aim of this paper is to study the consistency of the kernel density estimator pertaining to a continuous time stationary process X = (X-t)(t >= 0), with an underlying density f. More precisely, in a rather general dependency setting, where we use a martingale difference device and a technique based on a sequence of projections on sigma-fields, we establish the almost sure pointwise and uniform consistencies with rates of the estimate f(T) of f built upon the part (X-t)(0 <= t <= T) of the process X. (C) 2013 Elsevier B.V. All rights reserved.