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Invariance of Poisson Point Processes by Moment Identities with Statistical Applications

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Geometry and Invariance in Stochastic Dynamics (RTISD19 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 378))

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Abstract

This paper reviews nonlinear extensions of the Slivnyak-Mecke formula as moment identities for functionals of Poisson point processes, and some of their applications. This includes studying the invariance of Poisson point processes under random transformations, as well as applications to distribution estimation for random sets in stochastic geometry, random graph connectivity, and density estimation for neuron membrane potentials in Poisson shot noise models.

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Acknowledgements

The Mathematica code used to produce Figs. 4 and 6 was provided by A.P. Kartun-Giles.

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Authors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Nanyang Link, 637371, Singapore

    Nicolas Privault

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  1. Nicolas Privault
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Correspondence to Nicolas Privault .

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Editors and Affiliations

  1. Department of Mathematics, Università degli Studi di Milano, Milan, Italy

    Stefania Ugolini

  2. Department of Mathematics, Università degli Studi di Milano, Milan, Italy

    Marco Fuhrman

  3. Department of Economics, Università degli Studi dell'Insubria, Varese, Italy

    Elisa Mastrogiacomo

  4. Department of Agricultural and Environmental Sciences, Università degli Studi di Milano, Milan, Italy

    Paola Morando

  5. Mathematic and Informatic Department, Bergische Universität Wuppertal, Wuppertal, Germany

    Barbara Rüdiger

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Privault, N. (2021). Invariance of Poisson Point Processes by Moment Identities with Statistical Applications. In: Ugolini, S., Fuhrman, M., Mastrogiacomo, E., Morando, P., Rüdiger, B. (eds) Geometry and Invariance in Stochastic Dynamics. RTISD19 2019. Springer Proceedings in Mathematics & Statistics, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-030-87432-2_13

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