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April 1999 Palm Measure Duality and Conditioning in Regenerative Sets
Olav Kallenberg
Ann. Probab. 27(2): 945-969 (April 1999). DOI: 10.1214/aop/1022677391


For a simple point process $\Xi$ on a suitable topological space, the associated Palm distribution at a point s may be approximated by the conditional distribution, given that $\Xi$ hits a small neighborhood of $s$. To study the corresponding approximation problem for more general random sets, we develop a general duality theory, which allows the Palm distributions with respect to an associated random measure to be expressed in terms of conditional densities with suitable martingale and continuity properties. The stated approximation property then becomes equivalent to a certain asymptotic relation involving conditional hitting probabilities. As an application, we consider the Palm distributions of regenerative sets with respect to their local time random measures.


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Olav Kallenberg. "Palm Measure Duality and Conditioning in Regenerative Sets." Ann. Probab. 27 (2) 945 - 969, April 1999.


Published: April 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0953.60037
MathSciNet: MR1698987
Digital Object Identifier: 10.1214/aop/1022677391

Primary: 60G57
Secondary: 60J55

Keywords: conditional densities and hitting probabilities , Local time , Palm distributions , Random sets and measures , set-indexed martingales

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 2 • April 1999
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