Nearest-Neighbour Markov Point Processes on Graph with Euclidean Edges

M.N.M. van Lieshout (Corresponding Author)

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We define nearest-neighbour point processes on graphs with Euclidean edges and linear networks. They can be seen as analogues of renewal processes on the real line. We show that the Delaunay neighbourhood relation on a tree satisfies the Baddeley‒Møller consistency conditions and provide a characterisation of Markov functions with respect to this relation. We show that a modified relation defined in terms of the local geometry of the graph satisfies the consistency conditions for all graphs with Euclidean edges that do not contain triangles.
Original languageEnglish
Pages (from-to)1275-1293
Number of pages19
JournalAdvances in applied probability
Issue number4
Publication statusPublished - 1 Dec 2018


  • Graph with Euclidean edges
  • Linear network
  • Markov point process
  • Nearest-neighbour interaction
  • Renewal process
  • Delaunay neighbour

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