Convergence of thinning processes using compensators

Fred Böker

Stochastic Processes and their Applications, 1986, vol. 23, issue 1, 143-152

Abstract: In this paper the convergence of suitably normalized thinning processes is considered. That is, the convergence in distribution of point processes of the form [eta] = [Sigma][infinity]j = 1Xj[delta]j, where Xj are 0-1 veriables. A sufficient condition for convergence towards a Poisson process is used for Markovian thinning, thinning by success runs in a Bernoulli process or by special patterns in a renewal process and by high level exceedances of a stationary sequence of random variables. The condition is that simple sums of conditional probabilities of the Xj's, also suitably normalized, converge to the identity mapping on .

Keywords: point; processes; thinning; convergence; to; Poisson; compensators (search for similar items in EconPapers)
Date: 1986
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