A sufficient condition for association of a renewal process. (English) Zbl 0608.60084

Burton, Robert M. jun.; Waymire, Ed

Ann. Probab. 14, 1272-1276 (1986).

Let N be a renewal point process on [0,\(\infty)\) with life time density f and consider the family \({\mathcal F}\) of random variables N(A), A Borel subset of [0,\(\infty)\). The authors prove that \({\mathcal F}\) is ”associated” [see C. M. Newman, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 361- 371 (1982; Zbl 0465.60010)] provided log f is a convex function. Interesting connections to reliability theory and to particle systems are stated.

Reviewer: H.Wegmann

MSC:

60K05	Renewal theory
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

associated variables; failure rate; renewal point process; reliability theory; particle systems

Citations:

Zbl 0465.60010