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Point-shift foliation of a point process

Baccelli, F ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1214/17-EJP123
  3. Publisher: University of Washington , 2018
  4. Abstract:
  5. A point-shift F maps each point of a point process Φ to some point of Φ. For all translation invariant point-shifts F, the F-foliation of Φ is a partition of the support of Φ which is the discrete analogue of the stable manifold of F on Φ. It is first shown that foliations lead to a classification of the behavior of point-shifts on point processes. Both qualitative and quantitative properties of foliations are then established. It is shown that for all point-shifts F, there exists a point-shift F⊥, the orbits of which are the F-foils of Φ, and which is measure-preserving. The foils are not always stationary point processes. Nevertheless, they admit relative intensities with respect to one another. © 2018, University of Washington. All rights reserved
  6. Keywords:
  7. Allocation rule ; Dynamical system ; Mass transport principle ; Palm probability ; Point process ; Point-map ; Point-shift ; Stable manifold ; Stationarity
  8. Source: Electronic Journal of Probability ; Volume 23 , 2018 ; 10836489 (ISSN)
  9. URL: https://arxiv.org/abs/1601.03653