Consistency results for the kernel density estimate on continuous time stationary and dependent data

Abstract: The aim of this paper is to study the consistency of the kernel density estimator pertaining to a continuous time stationary process , with an underlying density . 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 -fields, we establish the almost sure pointwise and uniform consistencies with rates of the estimate of built upon the part of the process . [Copyright &y& Elsevier]