Sufficient conditions for long-range count dependence of stationary point processes on the real line (Q2748447)

\textit{D. J. Daley} and \textit{R. Vesilo} [Stochastic Processes Appl. 70, No. 2, 265-282 (1997; Zbl 0911.60077)] introduced long-range count dependence (LRcD) for stationary point processes on the real line and discussed some relevant results on renewal processes and queueing output processes. \textit{D. J. Daley} [Ann. Probab. 27, No. 4, 2035-2041 (1999; Zbl 0961.60083)] subsequently showed that a necessary and sufficient condition for a stationary renewal process to be LRcD is that under its Palm measure the generic lifetime distribution has infinite second moment. The article that we are now reviewing shows amongst other things that point processes dominating, in a sense of stochastic ordering, LRcD point processes are themselves LRcD, and that for a point process to be LRcD it is not necessary that the corresponding second Palm moment of interpoint distances be infinite.