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Convergence of thinning processes using compensators

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  • Böker, Fred

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 .

Suggested Citation

  • Böker, Fred, 1986. "Convergence of thinning processes using compensators," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 143-152, October.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:1:p:143-152
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