Ordered thinnings of point processes and random measures

摘要: Abstract This is a study of thinnings point processes and random measures on the real line that satisfy weak law large numbers. The thinning procedures have dependencies based order points or masses being thinned such process composition two measures. It shown (normalized by certain function) converges in distribution if only does. result used to characterize convergence infinitely divisible processes, as compound Poisson process, when independent nonhomogeneous, stationary, Markovian, regenerative. Thinning sequence identically distributed operations also discussed. results here contain Renyi's classical theorem many its extensions.