Iterated Palm Conditioning and Some Slivnyak-Type Theorems for Cox and Cluster Processes

Olav Kallenberg ()
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Olav Kallenberg: Auburn University

Journal of Theoretical Probability, 2011, vol. 24, issue 3, 875-893

Abstract: Abstract A huge literature is devoted to extensions and ramifications of Slivnyak’s celebrated theorem—the fact that a point process on a Borel space is Poisson if and only if its reduced Palm distributions agree almost everywhere with the original distribution. Here we prove some multivariate versions of the mentioned property for randomizations and Cox processes. This leads to Slivnyak-type theorems for certain Cox cluster processes, arising naturally both in exchangeability theory and in the context of superprocesses. Our proofs are based on a general iteration principle, which enables us to calculate Palm measures via a preliminary conditioning.

Keywords: Iterated conditioning; Random measures and point processes; Multivariate Palm measures; Randomizations and Cox processes; Cluster processes; Exchangeable processes; 60G57; 60A10; 60G09 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0295-6

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