Some distributional results for Poisson-Voronoi tessellations

Advances in Applied Probability

Volumn 39, Issue 1, 2007, Pages 16-40

  Baumstark, Volker ^a   Last, Günter ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Palm distribution; Poisson process; Random measure; Typical edge; Typical face; Voronoi tessellation

Indexed keywords

IMAGE PROCESSING; MATHEMATICAL MODELS; RANDOM PROCESSES;

PALM DISTRIBUTION; POISSON PROCESS; VORONOI TESSELLATION;

POISSON DISTRIBUTION;

EID: 34247562716     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1175266467     Document Type: Article

References (11)

1. ASMUSSEN, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.
2. KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd edn. Springer, New York.
3. MECKE, J. (1967). Stationäre zufällige Maße auf lokalkompakten Abelschen Gruppen. Z. Wahrscheinlichkeitsth. 9, 36-58.
4. MECKE, J. AND MUCHE, L. (1995). The Poisson Voronoi tessellation. I. A basic identity. Math. Nachr. 176, 199-208.
5. MILES, R. (1974). A synopsis of 'Poisson flats in Euclidean spaces'. In Stochastic Geometry, eds E. F. Harding and D, G. Kendall, John Wiley, New York, pp. 202-227.
6. d. Adv. Appl. Prob. 21, 37-73.
7. MØLLER, J. (1994). Lectures on Random Voronoi Tessellations (Lecture Notes Statist. 87). Springer, New York.
8. MUCHE, L. (2005). The Poisson-Voronoi tessellation: relationships for edges. Adv. Appl. Prob. 37, 279-296.
9. NEVEU, J. (1977). Processus ponctuels. In École d'Eté de Probabilités de Saint-Flour VI (Lecture Notes Math. 598). Springer, Berlin, pp. 249-445.
10. SCHNEIDER, R. AND WEIL, W. (2000). Stochastische Geometrie. Teubner, Stuttgart.
11. STOYAN, D., KENDALL, W. S. AND MECKE, J. (1995). Stochastic Geometry and Its Applications, 2nd edn. John Wiley, Chichester.