Exit spaces for Cox processes and the P\'olya sum process

For Cox processes we construct a Markov process with increasing paths to couple the condensations of the Cox process in a monotone way. A similar procedure procedure yields an analogue Markov process for the P\'olya sum process. Moreover, we identify the exit spaces of these Markov processes and identify them firstly as mixtures of certain extremal processes, i.e. as a process in a random environment, and secondly as Gibbs processes

The Logical Postulates of Boge, Carnap and Johnson in the Context of Papangelou Processes

Rafler M, Zessin HN. The Logical Postulates of Boge, Carnap and Johnson in the Context of Papangelou Processes. Journal of Theoretical Probability. 2015;28(4):1431-1446.We adapt Johnson's sufficiency postulate, Carnap's prediction invariance postulate and Boge's learn-merge invariance to the context of Papangelou processes and discuss equivalence of their generalizations, in particular their weak and strong generalizations. This discussion identifies a condition which occurs in the construction of Papangelou processes. In particular, we show that these generalizations characterize classes of Poisson and Plya point processes