Summary
In this paper we characterize the, what we call, visible projection of a point process on an arbitrary space as a Radon-Nikodym-derivative in the same manner the dual previsible projection of a process on ℝ+ is defined by Dellacherie and Meyer [1]; this visible projection turns out to coïncide with the conditional intensity as defined by Papangelou [3]; a neat behaviour is imposed to the point process by only one intuïtively clear condition, which is proved to be equivalent to the classical smoothnessconditions (∑) and (∑*).
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Bibliographie
Dellacherie, C., Meyer, P.A.: Probabilités et potentiel. Chapitres I à IV (1975) et Chapitres V à VIII. (1980). Paris: Hermann
Kallenberg, O.: On conditional intensities of point processes. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 41, 205–220 (1978)
Papangelou, F.: The conditional intensity of general point processes and an application to line processes. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 28, 207–226 (1974)
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Ces recherches ont été subventionées par l'Organisation Néerlandaise pour le Développement de la Recherche Scientifique (Z.W.O.; nℴ de bourse 62–138) et partiellement par le Centre National de la Recherche Scientifique
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van der Hoeven, P.C.T. Une projection de processus ponctuels. Z. Wahrscheinlichkeitstheorie verw Gebiete 61, 483–499 (1982). https://doi.org/10.1007/BF00531619
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DOI: https://doi.org/10.1007/BF00531619