Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency

Let Z:={Zt,t≥0} be a stationary Gaussian process. We study two estimators of E[Z02], namely fˆT(Z):=1 T ∫0TZt2dt, and f˜n(Z):=1 n ∑i=1nZti2, where ti=iΔn, i=0,1,…,n, Δn→0 Tn:=nΔn→∞. prove that the are strongly consistent establish Berry-Esseen bounds for central limit theorem involving fˆT(Z) f˜n(Z). apply these results to asymptotically processes estimate drift parameter Ornstein-Uhlenbeck processes.