Adaptive sampling schemes for density estimation

In this paper, first we propose sharp sampling schemes for nonparametric density estimation for discretely observed continuous time processes. Next, since such samplings depend on two coefficients: γ0γ0, r0r0 linked with regularity of the underlying sample paths and the density, respectively, we give and study the pointwise asymptotic behaviour of an adaptive kernel estimator in the case of known γ0γ0 and unknown r0r0. Finally, we propose a procedure in the case of both coefficients unknown.