Supporting-points processes and some of their applications

Probability Theory and Related Fields

Volumn 117, Issue 2, 2000, Pages 163-182

  Baryshnikov, Yu ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034374793     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050002     Document Type: Article

References (21)

1. Affentranger, F., Wieacker, J.A.: On the Convex Hulls of Uniform Random Points, Discr. Comp. Geometry, 6, 291-305 (1991)
2. Alberevio, S., Molchanov, S., Surgalis, D.: Stratified structure of the Universe and Burger's equation - a probabilistic approach. Probab. Theory Relat. Fields, 100, 457-484 (1994)
3. Barndorf-Nielsen, O., Sobel, M.: On the distribution of the number of admissible points in a vector sample. Probab. Th. and Appl. 11, n.2 (1966)
4. Barany, I.: Intrinsic volumes and f-vectors of random polytopes. Math. Ann., 285, 671-699 (1989)
5. Barany, I., Larman, D.: Convex bodies, economic gap covering, random polytopes. Mathematika, 35, 274-291 (1988)
6. Baryshnikov, Yu.: On the distribution of the number of options non-dominated with respect to a binary relation (in Russian). Izvestija AN SSSR, Tekhn. kibernetika, n.3 1986
7. Brillinger, D.: Statistical inference for stationary point processes, In: Stochastic processes and related topics, Puri, M. (ed.), Academic Press, New York (1975)
8. Buchta, C.: Zufällige, Polyeder - Eine Übersicht. In: Zahlentheoretische Analysis, Hlawka, E. (ed.), LN in Math. 1114, Springer, Heidelberg (1985)
9. Cabo, J., Groenenboom, P.: Limit theorems for functional of convex hulls, Prob. Theory Relat. Fields, 100, 31-55 (1994)
10. Dwyer, R. A.: On the Convex Hull of Random Points in a Polytope. J. Appl. Probab., 25, 688-699 (1988)
11. Groeneboom, P.: Limit theorems for convex hulls, Prob. Theory Relat. Fields, 79, 327-368 (1988)
12. Gurbatov, S., Malakhov, A., Saichev, A.: Nonlinear random waves and turbulence in nondispersive media: waves, rays, particles. Manchester UP, Manchester (1991)
13. Hueter, I.: The convex hull of n random points and its vertex process. PhD Thesis, U of Berne (1992)
14. Ivanin, V.M.: Computation of the variance of the number of elements of Pareto set for a vector sample with independent components (In Russian). In: Problemy Optimizacii, Naukova Dumka, Kiev (1976)
15. Ivanoff, G.: Central limit theorems for point processes. Stoch. Proc. Appl., 12, 171-186 (1982)
16. Møller, J.: Lectures on random Voronoi tessellations. (Lecture notes in statistics; 87) Springer, Heidelberg 1994
17. Molchanov, S., Surgulis, D., Woyczinski, W.: Hyperbolic asymptotics in Burger's turbulence and extremal processes, Comm. Math. Physics, 168, 209-226 (1995)
18. Postnikov, A.: Tauberian theory and its applications. AMS, Providence (1980)
19. Ruelle, D.: Statistical Mechanics: Rigorous Results. W. Benjamin, Amsterdam (1970)
20. Schneider, R.: Random Approximations of Convex Sets. J. of Microscopy, 151, 211-227 (1988)
21. Van Wel, B.: The convex hull of a uniform sample from the interior of a simple d-polytope. J. Appl. Prob., 26, 259-273 (1989)