Invariance of Poisson point processes by moment identities with statistical applications. (English) Zbl 1499.60157
Ugolini, Stefania (ed.) et al., Geometry and invariance in stochastic dynamics. Selected papers based on the presentations at the the conference on random transformations and invariance in stochastic dynamics, Verona, Italy, March 25–29, 2019. Cham: Springer. Springer Proc. Math. Stat. 378, 247-265 (2021).
Summary: 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.
For the entire collection see [Zbl 1479.37003].
For the entire collection see [Zbl 1479.37003].
MSC:
| 60G57 | Random measures |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 60D05 | Geometric probability and stochastic geometry |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 60G48 | Generalizations of martingales |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
Keywords:
Poisson point process; moments; stochastic geometry; random-connection model; filtered shot noise processes; Gram-Charlier expansions; neuron membrane potentialsReferences:
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