Mean values of weighted cells of stationary poisson hyperplane tessellations of double-struck R signd

Mathematische Nachrichten

Volumn 193, Issue , 1998, Pages 37-48

  Favis, Wassilis ^a   Weiß, Viola ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Stochastic geometry, poisson hyperplane tessellation, anisotropy, mean values, second Order quantities, weighted cells, cell characteristics

Indexed keywords

EID: 0032412689     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19981930105     Document Type: Article

References (18)

1. AMBARTZUMIAN, R. V., MECKE, J., and STOYAN, D.: Geometrische Wahrscheinlichkeiten und Stochastische Geometrie, Akademie Verlag, Berlin, 1993
2. HANISCH, K. H.: On Inversion Formulae for n - Fold Palm Distributions of Point Processes in LCS - Spaces, Math. Nachr. 106 (1982), 171-179
3. KALLENBERG, O.: Random Measures, Akademie Verlag, Berlin, and Academic Press, London, 1983
4. MATHERON, G.: Random Sets and Integral Geometry, J. Wiley & Sons, New York/London, 1975
5. MECKE, J.: Das n - fache Campbell - Maß, Unpublished Manuscript, Jena, 1979
6. MECKE, J.: Inequalities for the Anisotropic Poisson Polytope, Adv. Appl. Prob 27(1995), 56-62
7. MECKE, J., SCHNEIDER, R., STOYAN, D., and WEIL, W.: Stochastische Geometrie, Birkhäuser Verlag, Basel/Boston/Berlin, 1990
8. MILES, R. E.: Random Polygons Determined by Random Lines in a Plane I, double-struck I sign, Proc. Natl. Acad. Sci. USA 52 (1964), 901-907, 1157-1160
9. MILES, R. E.: The Various Aggregates of Random Polygons Determined by Random Lines in the Plane, Advances in Math. 10 (1973), 256-290
10. d, Adv. Appl. Prob. 21 (1989), 37-73
11. ONIŠČIK, A. L., and SULANKE, R.: Algebra und Geometrie, Deutscher Verlag der Wissenschaften, Berlin, 1986
12. SANTALÓ, L. A.: Integral Geometry and Geometric Probability, Addison - Wesley, Reading (Mass.), 1976
13. SCHNEIDER, R.: Isoperimetric Inequalities for Infinite Hyperplane Systems, In "The László Fejes Tóth Festschrift" (eds. I. BÁRÁNY and J. PACH), Discrete Comput. Geom. 13 (1995), 609-627
14. SCHNEIDER, R., and WEIL, W.: Integralgeometrie, B.G. Teubner, Stuttgart, 1992
15. STOYAN, D., KENDALL, W. S., and MECKE, J.: Stochastic Geometry and its Applications, Akademie Verlag, Berlin, 1987
16. n, Überlagerungen und stereologische Probleme, Ph.D. Thesis, Friedrich - Schiller - Universität Jena, 1984
17. WEIL, W., and WIEACKER, J. A.: Stochastic Geometry. In: Handbook of Convex Geometry, Vol. B (eds. P.M. GRUBER and J. M. WILLS), pp. 1391-1438, Elsevier, Amsterdam, 1993
18. d, Stochastics and Stochastics Reports 55 (1995), 195-205