The P\'olya sum process: Limit theorems for conditioned random fields

Abstract

In \cite{hZ09}, Zessin constructed the so-called P\'olya sum process via partial integration technique. This process shares some important properties with the Poisson process such as complete randomness and infinite divisibility. This work discusses H-sufficient statistics for the P\'olya sum process as it was done for the Poisson process in \cite{hZ76}