Moment formulae for general point processes

TL;DR

This paper generalizes moment formulae for point processes using Papangelou intensities, enabling the calculation of moments of stochastic integrals and analyzing transformations of point processes.

Contribution

It introduces generalized moment formulae for arbitrary point processes based on Papangelou intensities, extending previous results.

Findings

Derived general formulas for moments of stochastic integrals of point processes

Applied these formulas to study transformations of point processes

Enhanced understanding of moment calculations in complex point process models

Abstract

The goal of this paper is to generalize most of the moment formulae obtained in [Pri11]. More precisely, we consider a general point process \mu, and show that the relevant quantities to our problem are the so-called Papangelou intensities. Then, we show some general formulae to recover the moment of order n of the stochastic integral of a random process. We will use these extended results to study a random transformation of the point process.