Uniform Convergence of Local Time and the Uniform Consistency of Density211 Estimators for Ergodic Diffusions

摘要

We prove a theorem on the uniform convergence of the local time of an ergodic211u001ediffusion. This result is then used to investigate certain estimators of the 211u001einvariant density of an ergodic diffusion, including kernel estimators. We show 211u001ethat the pointwise consistency of these estimators can be strengthened to uniform 211u001econsistency.