Strong Markov Property of Poisson Processes and Slivnyak Formula

  • Sergei Zuyev
Part of the Lecture Notes in Statistics book series (LNS, volume 185)


We discuss strong Markov property of Poisson point processes and the related stopping sets. Viewing Poisson process as a set indexed random field, we demonstrate how the martingale technique applies to establish the analogues of the classical results: Doob’s theorem, Wald identity in this multi-dimensional setting. In particular, we show that the famous Slivnyak-Mecke theorem characterising the Poisson process is a consequence of the strong Markov property.

Key words

Gamma-type result Poisson point process Slivnyak formula Strong Markov property 


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Copyright information

© Springer Science+Business Media Inc. 2006

Authors and Affiliations

  • Sergei Zuyev
    • 1
  1. 1.Department of Statistics and Modelling ScienceUniversity of StrathclydeGlasgowUK

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