No. 1097

Title:

Estimation for the invariant distribution of an ergodic diffusion process based on high frequency data

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Empirical distribution function, weak convergence, asymptotic efficiency.

Abstract:

    Let a one-dimensional ergodic diffusion process $ X $ be observed at time points $ 0=t_0^n < t_1^n < \cdots < t_n^n $ such that $ t_n^n \to \infty $ and $ n \Delta_n^{1+p}\to 0 $, where $ \Delta_n=\max_{1 \leq i \leq n}|t_i^n-t_{i-1}^n| $, with $ p \in (0,1) $ being a constant depending on a moment condition on $ X $. We prove that some empirical distribution functions based on this data are asymptotically normal and asymptotically efficient in a functional sense.