Palm distributions for log Gaussian Cox processes

TL;DR

This paper proves that the Palm distribution of a log Gaussian Cox process is also a log Gaussian Cox process with a modified intensity, enabling new analysis of process functionals.

Contribution

It establishes that the Palm distribution of a log Gaussian Cox process remains within the same class, differing only in intensity, which is a novel theoretical insight.

Findings

Palm distribution is a log Gaussian Cox process with altered intensity

Facilitates analysis of functional summaries for these processes

Provides a foundation for further statistical inference

Abstract

This paper establishes a remarkable result regarding Palmdistributions for a log Gaussian Cox process: the reduced Palmdistribution for a log Gaussian Cox process is itself a log Gaussian Coxprocess which only differs from the original log Gaussian Cox processin the intensity function. This new result is used to study functionalsummaries for log Gaussian Cox processes.