Edgeworth expansion for ergodic diffusions

The Edgeworth expansion for an additive functional of an ergodic diffusion is validated under fairly weak conditions. The validation procedure does not depend on the stationarity or the geometric mixing property, but exploits the strong Markov property of the process. In particular for an Itô-diffusion of dimension one, verifiable conditions for the validity of the expansion are given in terms of the coefficients of the corresponding stochastic differential equation. The maximum likelihood estimator for the CIR process is treated as example.