A Characterization of the Poisson Process revisited
Benjamin Nehring
TL;DR
This paper revisits the Poisson process, demonstrating that its splitting-characterization naturally follows from the Mecke-formula, thus providing a new perspective on its fundamental properties.
Contribution
It establishes that the splitting-characterization of the Poisson process is a direct consequence of the Mecke-formula, offering a simplified proof and deeper insight.
Findings
Splitting-characterization follows from the Mecke-formula
Provides a new perspective on Poisson process properties
Simplifies understanding of Poisson process characterization
Abstract
We show that the splitting-characterization of the Poisson point process is an immediate consequence of the Mecke-formula.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Point processes and geometric inequalities · Random Matrices and Applications