Palm Measure Invariance and Exchangeability for Marked Point Processes

Abstract

A random measure $\xi$ on a real interval $I$ is known to be exchangeable iff suitably reduced versions of the Palm distributions $Q_{t}$ are independent of $t \in I$. In this dissertation we prove a corresponding result where $\xi$ is a point process on $I$ with marks in some Borel space. For this case, the Palm distributions $Q_{s,t}$ depend on parameters $s \in S$ and $t \in I$, and we show that $\xi$ is exchangeable iff the reduced versions of $Q^{\prime}_{s,t}$ are independent of $t$.