Decomposition of gamma-distributed domains constructed from poisson point processes

Advances in Applied Probability

Volumn 35, Issue 1, 2003, Pages 56-69

  Cowan, Richard ^a   Quine, Malcolm ^a   Zuyev, Sergei ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Delaunay triangulation; Gamma type results; Poisson process; Set indexed martingale; Slivnyak theorem; Stopping set; Voronoi tessellation

Indexed keywords

ALGORITHMS; MARKOV PROCESSES; MATHEMATICAL MODELS; RANDOM PROCESSES; SET THEORY; THEOREM PROVING;

DELAUNAY TESSELATIONS; DELAUNAY TRIANGULATION; POISSON POINT PROCESS; SLIVNYAK THEORY; VORONOI TESSELLATIONS;

POISSON DISTRIBUTION;

EID: 0037357810     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1046366099     Document Type: Article

References (14)

1. Baccelli, F., Tchoumatchenko, K. and Zuyev, S. (2000). Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks. Adv. Appl. Prob. 32, 1-18.
2. Cowan, R. (2000). Some Delaunay circumdisks and related lunes. Tech. Rep., University of Sydney. Available at http://www.maths.usyd.edu.au/u/richardc/.
3. Hayen, A. and Quine, M. P. (2002). Areas of components of a Voronoi polygon in a homogeneous Poisson process in the plane. Adv. Appl. Prob. 34, 281-291.
4. Kurtz, T. (1980). The optional sampling theorem for martingales indexed by directed sets. Ann. Prob. 8, 675-681.
5. Mecke, J. (1967). Stationäre zufällige Masse auf localcompakten Abelischen Gruppen. Z. Wahrscheinlichkeitsth. 9, 36-58.
6. Mecke, J. and Muche, L. (1995). The Poisson Voronoi tessellation I. A basic identity. Math. Nachr. 176, 199-208.
7. Mecke, J. and Muche, L. (1996). The Poisson Voronoi tessellation II. Edge length distribution functions. Math. Nachr. 178, 271-283.
8. Miles, R. (1970). On the homogeneous planar Poisson process. Math. Biosci. 6, 85-127.
9. Miles, R. and Maillardet, R. (1982). The basic structures of Voronoi and generalized Voronoi polygons. in Essays in Statistical Science (J. Appl. Prob. Spec. Vol. 19A), eds J. Gani and E. J. Hannan, Applied Probability Trust, Sheffield, pp. 97-111.
10. Møller, J. and Zuyev, S. (1996). Gamma-type results and other related properties of Poisson processes. Adv. Appl. Prob. 28, 662-673.
11. Quine, M. P. and Watson, D. (1984). Radial generation of n-dimensional Poisson processes. J. Appl. Prob. 21, 548-557.
12. Rozanov, Y. A. (1982). Markov Random Fields. Springer, New York.
13. Slivnyak, I. (1962). Some properties of stationary flows of homogeneous random events. Teor. Veroyat. Primen. 7, 347-352 (in Russian). English translation: Theory Prob. Appl. 7, 336-341.
14. Zuyev, S. (1999). Stopping sets: gamma-type results and hitting properties. Adv. Appl. Prob. 31, 355-366.