Using renewal processes to generate long-range dependence and high variability. (English) Zbl 0601.60085

Dependence in probability and statistics, Conf. Oberwolfach 1985, Prog. Probab. Stat. 11, 73-89 (1986).
[For the entire collection see Zbl 0591.00012.]
Six theorems exploring three types of convergence involving the normalized partial sums of the stationary renewal process (W(t), \(t\in {\mathbb{Z}})\) and of the non-stationary process (V(t), \(t\in {\mathbb{Z}})\) both introduced by B. B. Mandelbrot [Int. Econ. Rev. 10, 82-111 (1969; Zbl 0191.510)] are announced.
The results improve some previous results of the second author [High variability and long-range dependence: a modelling approach based on renewal sequences. M. Sc. Thesis, Cornell Univ. (1983)].
Reviewer: Şt.P.Niculescu


60K05 Renewal theory