Limit theorems for the convex hull of random points in higher dimensions

Transactions of the American Mathematical Society

Volumn 351, Issue 11, 1999, Pages 4337-4363

  Hueter, Irene ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

(sub super) martingales; Central limit theorem; Convex hull; Markovian jump process; Poisson point process; Rotationally invariant distributions

Indexed keywords

EID: 22844457314     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02499-x     Document Type: Article

References (14)

1. Aldous, D. J., Fristedt, J., Griffin, P. S. and Pruitt, W. E. (1991). The number of extreme points in the convex hull of a random sample. J. Appl. Prob. 28, 287-304. MR 92j:60022
2. Carnal, H. (1970). Die konvexe Hülle von n rotationssymmetrisch verteilten Punkten. Z. Wahrscheinlichkeitstheorie vcnv. Geb. 15, 168-176. MR 44:3367
3. Dwyer, R. A. (1991). Convex hulls of samples from spherically symmetric distributions. Discrete Appl. Math. 31, 113-132. MR 92i:60020
4. Efron, B. (1965). The convex hull of a random set of points. Biometrika 52, 331-343. MR 34:6820
5. Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York. MR 42:5292
6. Groeneboom, P. (1988). Limit theorems for convex hulls. Prob. Theory Rel. Fields 79, 327-368. MR 89j:60024
7. Hoeffding, W. (1963). Probability inequalities for'sums of bounded random variables. J. Amer. Statist. Assoc. 58, no. 301, 13-30. MR 26:1908
8. Hueter, I. (1992). The convex hull of n random points and its vertex process. Doctoral Dissertation, University of Berne.
9. Hueter, I. (1994). The convex hull of a normal sample. Adv. Appl. Prob. 26, 855-875. MR 96g:60018
10. Ibragimov, I. A. and Linnik, Y. V. (1971). Independent and stationary sequences of random variables. Groningen: Wolters Noordhoff. MR 48:1287
11. Kallenberg, O. (1983). Random Measures. Akademie Verlag Berlin. MR 87g:60048
12. Raynaud, H. (1970). Sur l'enveloppe convexe des nuages de points aléatoires dans R". J. Appl. Prob. 7, 35-48. MR 41:2736
13. Rényi, A. and Sulanke, R. (1963). Über die konvexe Hülle von n zufällig gewählten Punkten. Z. Wahrscheinlichkeitstheorie verw. Geb. 2, 75-84. MR 27:6190
14. Stroock, D. \V. (1975). Diffusion processes associated with Levy generators. Z. Wahrscheinlichkeitstheorie verw. Geb. 32, 209-244. MR 55:6587