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- W1601019919 abstract "A compatible point-shift f maps, in a translation invariant way, each point of a stationary point processto some point of �. It is fully determined by its associated point-map, g f , which gives the image of the origin by f. The initial question of this paper is whether there exist probability measures which are left invariant by the translation of −g f . The point-map probabilities ofare defined from the action of the semigroup of point-map translations on the space of Palm prob- abilities, and more precisely from the compactification of the orbits of this semigroup action. If the point-map probability is uniquely de- fined, and if it satisfies certain continuity properties, it then provides a solution to the initial question. Point-map probabilities are shown to be a strict generalization of Palm probabilities: when the considered point-shift f is bijective, the point-map probability ofboils down to the Palm probability of �. When it is not bijective, there exist cases where the point-map probability ofis absolutely continuous with respect to its Palm probability, but there also exist cases where it is singular with respect to the latter. A criterium of existence of the point-map probabilities of a stationary point process is also provided. The results are illustrated by a few examples." @default.
- W1601019919 created "2016-06-24" @default.
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- W1601019919 date "2014-01-01" @default.
- W1601019919 modified "2023-09-27" @default.
- W1601019919 title "Compactification of the Action of a Point-Map on the Palm Probability of a Point Process" @default.
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