Gamma-type results and other related properties of poisson processes

Advances in Applied Probability

Volumn 28, Issue 3, 1996, Pages 662-673

  Møller, Jesper ^a   Zuyev, Sergei ^b,c  

^a AALBORG UNIVERSITY   (Denmark)

^b Inst Natl Rech Info en Automat

^c INRIA   (France)

Author keywords

Complementary theorem; Delaunay tessellation; Gamma distribution; Hyperplane tessellations; Palm probabilities; Poisson flat processes; Poisson point processes; Slivnyak's theorem; Stochastic geometry; Tessellation characteristics; Voronoi tessellation

Indexed keywords

EID: 0001597523     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800046437     Document Type: Article

References (21)

1. BACCELLI, F. AND BRÉMAUD, P. (1993) Virtual customers in sensitivity and light traffic analysis via Campbell's formula for point processes. Adv. Appl. Prob. 25, 221-234.
2. BACCELLI, F., KLEIN, M. AND ZUYEV, S. A. (1995) Perturbation analysis of functionals of random measures. Adv. Appl. Prob. 27, 306-325.
3. BARNDORFF-NIELSEN, O. E. (1978) Information and Exponential Families in Statistical Theory. Wiley, Chichester.
4. BLASZCZYSZYN, B. (1993) Factorial moment expansion for stochastic systems. Preprint. Mathematical Institute, Univeristy of Wroclaw.
5. DALEY, D. J. AND VERE-JONES, D. (1988) An Introduction to the Theory of Point Processes. Springer, New York.
6. HOFFMANN-JØRGENSEN, J. (1994) Probability with a View Toward Statistics. Vol. I. Chapman and Hall, New York.
7. MATHERON, G. (1975). Random Sets and Integral Geometry. Wiley, New York.
8. MECKE, J. (1967) Stationäre zufällige Masse auf lokalkompakten Abelschen Gruppen. Z. Wahrscheinlichkeitsth. 9, 36-58.
9. MILES, R. E. (1970) On the homogeneous planar Poisson point process. Math. Biosci. 6, 85-127.
10. MILES, R. E. (1971) Poisson flats in Euclidean spaces. Part II: Homogeneous Poisson flats and the complementary theorem. Adv. Appl. Prob. 3, 1-93.
11. MILES, R. E. (1972) The random division of space. Suppl. Adv. Appl. Prob. 243-266.
12. MILES, R. E. (1974) A synopsis of 'Poisson flats in Euclidean spaces'. In Stochastic Geometry ed. E. F. Harding and D. G. Kendall. Wiley, New York.
13. MILES, R. E. AND MAILLARDET, R. J. (1982) The basic structures of Voronoi and generalized Voronoi polygons. J. Appl. Prob. 19A, 97-111.
14. d. Adv. Appl. Prob. 21, 37-73.
15. MØLLER, J. (1992) Random Johnson-Mehl tessellations. Adv. Appl. Prob. 24, 814-844.
16. MØLLER, J. (1994) Lectures on Random Voronoi Tessellations. (Lecture Notes in Statistics 87.) Springer, New York.
17. SLIVNYAK, I. M. (1962) Some properties of stationary flows of homogeneous random events. Theory Prob. Appl. 7, 336-341.
18. STOYAN, D., KENDALL, W. S. AND MECKE, J. (1987) Stochastic Geometry and its Applications. Akademie, Berlin.
19. ZUYEV, S. A. (1992a) Estimates for distributions of the Voronoi polygon's geometric characteristics, Random Structures and Algorithms 3, 149-162.
20. ZUYEV, S. A. (1992b) Russo's formula for Poisson point fields and its applications. Disc. Math. 4, 118-129. (In Russian.) (Engl. transl.: Disc. Math. Appl. 3, 63-73.)
21. ZUYEV, S. A. (1992b) Russo's formula for Poisson point fields and its applications. Disc. Math. 4, 118-129. (In Russian.) (Engl. transl.: Disc. Math. Appl. 3, 63-73.)