Exit spaces for Cox processes and the Pólya sum process

2013/06/19 by Mathias Rafler, Rafler, Mathias
Computer Science · Decision Sciences · Mathematics · #60G55 #60J25 #60K35 #60K37 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1306.4578

openalex publication_date 2013/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Pólya 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.

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