Given a weakly dependent stationary process, we describe the transition between Berry-Esseen bound and second order Edgeworth expansion in terms of characteristic. This characteristic is sharp: We show that expansions are valid if only certain magnitude. If this not case, still get an optimal bound, thus describing exact transition. also obtain (fractional) given <inline-formula content-type="m...

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 pro...

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suita...