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

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.)

Zbl 0465.60010
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