Gamma-type results and other related properties of Poisson processes

@article{Mller1996GammatypeRA,
  title={Gamma-type results and other related properties of Poisson processes},
  author={Jesper M{\o}ller and Sergei A. Zuyev},
  journal={Advances in Applied Probability},
  year={1996},
  volume={28},
  pages={662 - 673}
}
Families of Poisson processes defined on general state spaces and with the intensity measure scaled by a positive parameter are investigated. In particular, mean value relations with respect to the scale parameter are established and used to derive various Gamma-type results for certain geometric characteristics determined by finite subprocesses. In particular, we deduce Miles' complementary theorem. Applications of the results within stochastic geometry and particularly for random… 
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