Gamma-type results and other related properties of Poisson processes
- 1 March 1996
- journal article
- stochastic geometry-and-statistical-applications
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 28 (03) , 662-673
- https://doi.org/10.1017/s0001867800046437
Abstract
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 tessellations are discussed.Keywords
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