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

Taqqu, Murad S.; Levy, Joshua B.

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

MSC:

60K05

Renewal theory

Keywords:

types of convergence; normalized partial sums of the stationary renewal process

Citations:

Zbl 0591.00012; Zbl 0191.510