Strong Markov Property of Poisson Processes and Slivnyak Formula
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 wordsGamma-type result Poisson point process Slivnyak formula Strong Markov property
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