DENSITY-ESTIMATION UNDER LONG-RANGE DEPENDENCE

Dehling and Taqqu established the weak convergence of the empirical pr ocess for a long-range dependent stationary sequence under Gaussian su bordination. We show that the corresponding density process, based on kernel estimators of the marginal density, converges weakly with the s ame normalization to the derivative of their limiting process. The phe nomenon, which carries on for higher derivatives and for functional la ws of the iterated logarithm, is in contrast with independent or weakl y dependent situations, where the density process cannot be tight in t he usual function spaces with supremum distances.