Minkowski functionals of Poisson processes
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This paper treats Poisson processes N with the convex ring S as state space, having a translation and rotation invariant intensity measure μ. Fixing a test set S 0∈S, denoting by Qk the random set of all points covered by N at least k times and collecting the Minkowski functionals in a generating function V, a simple formula is derived for the expectation of V(S 0 ∩Q k ) under an adequate moment condition on μ. This formula reflects the Poisson character of the process and extends to intersections of finite families of independent Poisson processes.
Markov processes, finite families of independent Poisson processes, Minkowski functionals, Point processes (e.g., Poisson, Cox, Hawkes processes), rotation invariant intensity measure
Markov processes, finite families of independent Poisson processes, Minkowski functionals, Point processes (e.g., Poisson, Cox, Hawkes processes), rotation invariant intensity measure
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