메뉴 건너뛰기




Volumn 47, Issue 1, 2003, Pages 79-90

Limit theorems for certain functionals of unions of random closed sets

Author keywords

Convex hulls; Extreme values; Hitting functionals; Mean width; Perimeter; Random sets; Unions of closed sets

Indexed keywords


EID: 0037268864     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97979494     Document Type: Article
Times cited : (2)

References (17)
  • 1
    • 0039346828 scopus 로고    scopus 로고
    • On the area and perimeter of a random convex hull in a bounded convex set
    • H. BRÄKER AND T. HSING, On the area and perimeter of a random convex hull in a bounded convex set, Probab. Theory Related Fields, 111 (1998), pp. 517-550.
    • (1998) Probab. Theory Related Fields , vol.111 , pp. 517-550
    • Bräker, H.1    Hsing, T.2
  • 2
    • 21844507773 scopus 로고
    • Limit theorems for functional of convex hulls
    • A. J. CABO AND P. GROENEBOOM, Limit theorems for functional of convex hulls, Probab. Theory Related Fields, 100 (1994), pp. 31-55.
    • (1994) Probab. Theory Related Fields , vol.100 , pp. 31-55
    • Cabo, A.J.1    Groeneboom, P.2
  • 3
    • 0000788596 scopus 로고
    • The convex hull of a random set of points
    • B. EFRON, The convex hull of a random set of points, Biometrika, 52 (1965), pp. 331-343.
    • (1965) Biometrika , vol.52 , pp. 331-343
    • Efron, B.1
  • 4
  • 5
    • 0001673399 scopus 로고
    • On the asymptotic distribution of the area outside a random convex hull in a disk
    • T. HSING, On the asymptotic distribution of the area outside a random convex hull in a disk, Ann. Appl. Probab., 4 (1994), pp. 478-493.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 478-493
    • Hsing, T.1
  • 7
    • 0002516161 scopus 로고
    • Limiting distributions for functional of the convex hull generated by uniformly distributed variables
    • in Russian
    • I. M. KHAMDAMOV AND A. V. NAGAEV, Limiting distributions for functional of the convex hull generated by uniformly distributed variables, Dokl. Akad. Nauk UzSSR, 7 (1991), pp. 8-9 (in Russian).
    • (1991) Dokl. Akad. Nauk UzSSR , vol.7 , pp. 8-9
    • Khamdamov, I.M.1    Nagaev, A.V.2
  • 8
    • 0001008606 scopus 로고
    • On the approximation of a ball by random polytopes
    • K. H. KÜFER, On the approximation of a ball by random polytopes, Adv. Appl. Probab., 26 (1994), pp. 876-892.
    • (1994) Adv. Appl. Probab. , vol.26 , pp. 876-892
    • Küfer, K.H.1
  • 10
    • 0003247552 scopus 로고
    • Limit theorems for unions of random closed sets
    • Springer-Verlag, Berlin, Heidelberg
    • I. S. MOLCHANOV, Limit Theorems for Unions of Random Closed Sets, Lecture Notes in Math. 1561, Springer-Verlag, Berlin, Heidelberg, 1993.
    • (1993) Lecture Notes in Math. , vol.1561
    • Molchanov, I.S.1
  • 11
    • 21444449512 scopus 로고
    • On the convergence of random processes generated by polyhedral approximation of convex compacts
    • I. S. MOLCHANOV, On the convergence of random processes generated by polyhedral approximation of convex compacts, Theory Probab. Appl., 40 (1995), pp. 383-390.
    • (1995) Theory Probab. Appl. , vol.40 , pp. 383-390
    • Molchanov, I.S.1
  • 13
    • 0001888582 scopus 로고
    • Über die konvexe hülle von n zufällig gewählten Punkten. I, II
    • A. RÉNYI AND R. SULANKE, Über die konvexe Hülle von n zufällig gewählten Punkten. I, II, Z. Wahrsch. Verw. Gebiete, 2 (1963), pp. 75-84; 3 (1964), pp. 138-147.
    • (1963) Z. Wahrsch. Verw. Gebiete , vol.2 , pp. 75-84
    • Rényi, A.1    Sulanke, R.2
  • 14
    • 4243406573 scopus 로고
    • A. RÉNYI AND R. SULANKE, Über die konvexe Hülle von n zufällig gewählten Punkten. I, II, Z. Wahrsch. Verw. Gebiete, 2 (1963), pp. 75-84; 3 (1964), pp. 138-147.
    • (1964) Z. Wahrsch. Verw. Gebiete , vol.3 , pp. 138-147
  • 16
    • 84986685654 scopus 로고
    • Random approximation of convex sets
    • R. SCHNEIDER, Random approximation of convex sets, J. Microscopy, 151 (1988), pp. 211-227.
    • (1988) J. Microscopy , vol.151 , pp. 211-227
    • Schneider, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.