Factorial moments of point processes

TL;DR

This paper derives simplified joint factorial moment identities for point processes with Papangelou intensities, including Poisson processes, and explores their applications to transformations and distribution invariance.

Contribution

It introduces a simplified proof for factorial moment identities and extends them to Poisson point processes and their transformations.

Findings

Simplified derivation of joint factorial moment identities.

Extension of identities to Poisson point processes.

Applications to transformations and invariance properties.

Abstract

We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous approaches to related moment identities and includes the setting of Poisson point processes. Applications are given to random transformations of point processes and to their distribution invariance properties.