Abstract
The purpose of the present paper is to characterize Campbell measures and Palm distributions of random measures and to apply these results in a new approach to the characterizations of infinitely divisible random measures by their Laplace functionals and their Palm distributions. The results on infinitely divisible random measures are well known. They can be found together with a detailed list of references in Kallenberg's monograph [2], which also contains proofs of almost all statements in Section 1 of this paper (see his note on page 9 concerning the Polish space setting).
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References
Jagers, P.: On Palm probabilities. Z. Wahrscheinlichkeitstheorie verw. Gebiete 26, 17–32 (1973)
Kallenberg, O.: Random measures. Berlin: Akademie-Verlag 1975
Krickeberg, K.: Processus spatiaux. Lecture notes. Universités Paris V, VI, 1975/76
Mecke, J.: StationÄre zufÄllige Ma\e auf lokalkompakten Hausdorffschen RÄumen. Z. Wahrscheinlichkeitstheorie verw. Gebiete 9, 36–58 (1967)
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Wegmann, H. Characterization of palm distributions and infinitely divisible random measures. Z. Wahrscheinlichkeitstheorie verw Gebiete 39, 257–262 (1977). https://doi.org/10.1007/BF00535477
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DOI: https://doi.org/10.1007/BF00535477