Stationary iterated tessellations

Advances in Applied Probability

Volumn 35, Issue 2, 2003, Pages 337-353

  Maier, Roland ^a   Schmidt, Volker ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Bernoulli thinning; Facet process; Intensity formula; Isotropy; Iteration; Nesting; Quermassdensity; Random tessellation; Stationarity; Stochastic geometry; Superposition; Typical facet

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; GEOMETRY; MATHEMATICAL MODELS; POISSON EQUATION; RANDOM PROCESSES;

FACET PROCESS; RANDOM TESSELLATION; STOCHASTIC GEOMETRY;

ITERATIVE METHODS;

EID: 0012952890     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1051201649     Document Type: Article

References (16)

1. Ambartzumian, R. V. (1990). Factorization Calculus and Geometric Probability. Cambridge University Press.
2. Baccelli, F., Gloaguen, C. and Zuyev, S. (2000). Superposition of Planar Voronoi Tessellations. Commun. Statist. Stoch. Models 16, 69-98.
3. Kendall, W. S. and Mecke, J. (1987). The range of the mean-value quantities of planar tessellations. J. Appl. Prob. 24, 411-421.
4. Maier, R. and Schmidt, V. (2002). Stationary iterated tessellations. Tech. Rep. University of Ulm. Available at http://www.mathematik.uni-ulm.de/stochastik/
5. Matheron, G. (1975). Random Sets and Integral Geometry. John Wiley: New York.
6. Mecke, J. (1981). Formulas for stationary planar fibre processes III - Intersections with fibre systems. Math. Operationsforsch. Statist. Ser. Statist. 12, 201-210.
7. Mecke, J. (1984). Parametric representation of mean values for stationary random mosaics. Math. Operations-forsch. Statist. Ser. Statist. 15, 437-442.
8. Miles, R. E. (1998). A large class of random tessellations with the class Poisson polygon distributions (abstract). Adv. Appl. Prob. 30, 285.
9. Miles, R. E. and Mackisack, M. S. (1996). Further random tessellations with the class Poisson polygon distributions (abstract). Adv. Appl. Prob. 28, 338-339.
10. Miles, R. E. and Mackisack, M. S. (2002). A large class of random tessellations with the class Poisson polygon distributions. Forma 17, 1-17.
11. d. Adv. Appl. Prob. 21, 37-73.
12. Nagel, W. and Weiss, V. (2003). Limits of sequences of stationary planar tessellations. Adv. Appl. Prob. 35, 123-138.
13. Santaló, L. A. (1984). Mixed random mosaics. Math. Nachr. 117, 129-133.
14. Schneider, R. and Weil, W. (2000). Stochastische Geometrie. Teubner. Stuttgart.
15. Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and Its Applications. John Wiley, Chichester.
16. Weiss, V. and Nagel, W. (1999). Interdependences of directional quantities of planar tessellations. Adv. Appl. Prob. 32, 664-678.