A CHARACTERIZATION OF G-PROCESSES AND THE POISSON PROCESSES IN Rn

摘要

It is proved in this paper that if each point of a stochastic point process in R (see l.l) is deleted vith probability r (0 .< p < 1) and retained -with probability q - 1-p (deletions beinrr independent) and the scale is magnified by 1/q the resulting stochastic point process tends to a Poisson process as q -*- 0 if and only if the initial process is veil-distributed (G-process, see l.l).