Efficient density estimation for ergodic diffusion processes (Q1962689)

The problem of asymptotically efficient estimation of the density of the invariant measure of a diffusion process is considered. An efficient estimator is defined by the minimax lower bound on the risk of all estimators. The author shows that the local-time and kernel-type estimators are asymptotically efficient for the loss functions with polynomial majorants. The asymptotic behavior of a wide class of unbiased estimators with the same limit variances is also discussed.