Summary
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.
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References
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Zuyev, S. (2006). Strong Markov Property of Poisson Processes and Slivnyak Formula. In: Baddeley, A., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (eds) Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, vol 185. Springer, New York, NY. https://doi.org/10.1007/0-387-31144-0_3
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DOI: https://doi.org/10.1007/0-387-31144-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-28311-1
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