메뉴 건너뛰기




Volumn 12, Issue , 2007, Pages 989-1035

Gaussian limits for random geometric measures

Author keywords

Central limit theorem; Gaussian field; Germ grain model; Point process; Random measure; Random set; Stabilization

Indexed keywords


EID: 34547700101     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v12-429     Document Type: Article
Times cited : (75)

References (27)
  • 1
    • 0000380180 scopus 로고
    • On central limit theorems in geometrical probability
    • F. Avram and D. Bertsimas (1993), On central limit theorems in geometrical probability. Ann. Appl. Probab. 3 1033-1046.
    • (1993) Ann. Appl. Probab , vol.3 , pp. 1033-1046
    • Avram, F.1    Bertsimas, D.2
  • 3
    • 14544281094 scopus 로고    scopus 로고
    • Gaussian limits for random measures in geometric probability
    • Yu. Baryshnikov and J. E. Yukich (2005). Gaussian limits for random measures in geometric probability. Ann. Appl. Probab. 15, 213-253.
    • (2005) Ann. Appl. Probab , vol.15 , pp. 213-253
    • Baryshnikov, Y.U.1    Yukich, J.E.2
  • 4
    • 0000467043 scopus 로고
    • Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test
    • P. J. Bickel and L. Breiman (1983). Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test. Ann. Probab. 11 (1983) 185-214.
    • (1983) Ann. Probab , vol.11 , pp. 185-214
    • Bickel, P.J.1    Breiman, L.2
  • 7
    • 12044256185 scopus 로고
    • Random and cooperative adsorption
    • J. W. Evans (1993). Random and cooperative adsorption, Reviews of Modern Physics, 65, 1281-1329.
    • (1993) Reviews of Modern Physics , vol.65 , pp. 1281-1329
    • Evans, J.W.1
  • 8
    • 0342581623 scopus 로고
    • M-dependent random fields with analytic cumulant generating function
    • F. Götze, L. Heinrich and C. Hipp (1995). m-dependent random fields with analytic cumulant generating function. Scand. J. Statist 22, 183-195.
    • (1995) Scand. J. Statist , vol.22 , pp. 183-195
    • Götze, F.1    Heinrich, L.2    Hipp, C.3
  • 10
    • 0007225034 scopus 로고
    • Asymptotic properties of minimum contrast estimators for parameters of Boolean models
    • L. Heinrich (1993). Asymptotic properties of minimum contrast estimators for parameters of Boolean models. Metrika 40, 67-94.
    • (1993) Metrika , vol.40 , pp. 67-94
    • Heinrich, L.1
  • 11
    • 0033141155 scopus 로고    scopus 로고
    • Central limit theorem for a class of random measures associated with germ-grain models
    • L. Heinrich and I. Molchanov (1999). Central limit theorem for a class of random measures associated with germ-grain models. Adv. Appl. Probab. 31, 283-314.
    • (1999) Adv. Appl. Probab , vol.31 , pp. 283-314
    • Heinrich, L.1    Molchanov, I.2
  • 12
    • 0003523893 scopus 로고
    • Oxford Universiy Press (Oxford Studies in Probability 3)
    • J.F.C. Kingman, (1993). Poisson Processes. Oxford Universiy Press (Oxford Studies in Probability 3).
    • (1993) Poisson Processes.
    • Kingman, J.F.C.1
  • 13
    • 0037708521 scopus 로고
    • Asymptotic properties of stereological estimators of volume fraction for stationary random sets
    • S. Mase (1982). Asymptotic properties of stereological estimators of volume fraction for stationary random sets. J. Appl. Probab. 19 111-126.
    • (1982) J. Appl. Probab , vol.19 , pp. 111-126
    • Mase, S.1
  • 14
    • 0033210542 scopus 로고    scopus 로고
    • Asymptotics for Voronoi tessellations on random samples
    • K. McGivney and J. E. Yukich (1999). Asymptotics for Voronoi tessellations on random samples. Stochastic Process. Appl. 83 273-288
    • (1999) Stochastic Process. Appl. , vol.83 , pp. 273-288
    • Mc Givney, K.1    Yukich, J.E.2
  • 16
    • 0000594254 scopus 로고
    • Asymptotic properties of estimators for parameters of the Boolean model
    • I. Molchanov and D. Stoyan (1994). Asymptotic properties of estimators for parameters of the Boolean model. Adv. Appl. Probab. 26, 301-323.
    • (1994) Adv. Appl. Probab. , vol.26 , pp. 301-323
    • Molchanov, I.1    Stoyan, D.2
  • 17
    • 0012535670 scopus 로고    scopus 로고
    • Oxford University Press (Oxford Studies in Probability 5)
    • M. Penrose (2003). Random Geometric Graphs. Oxford University Press (Oxford Studies in Probability 5).
    • (2003) Random Geometric Graphs.
    • Penrose, M.1
  • 18
    • 27644525072 scopus 로고    scopus 로고
    • Multivariate spatial central limit theorems with applications to percolation and spatial graphs
    • M. D. Penrose (2005). Multivariate spatial central limit theorems with applications to percolation and spatial graphs. Ann. Probab. 33, 1945-1991.
    • (2005) Ann. Probab , vol.33 , pp. 1945-1991
    • Penrose, M.D.1
  • 20
    • 33745946243 scopus 로고    scopus 로고
    • On the total length of the random minimal directed spanning tree
    • M.D. Penrose and A.R. Wade (2006). On the total length of the random minimal directed spanning tree. Adv. Appl. Probab. 38, 336-372.
    • (2006) Adv. Appl. Probab , vol.38 , pp. 336-372
    • Penrose, M.D.1    Wade, A.R.2
  • 21
    • 0035497809 scopus 로고    scopus 로고
    • Central limit theorems for some graphs in computational geometry
    • M.D. Penrose and J.E. Yukich (2001). Central limit theorems for some graphs in computational geometry. Ann. Appl. Probab. 11, 1005-1041.
    • (2001) Ann. Appl. Probab , vol.11 , pp. 1005-1041
    • Penrose, M.D.1    Yukich, J.E.2
  • 22
    • 0036117358 scopus 로고    scopus 로고
    • Limit theory for random sequential packing and deposition
    • M.D. Penrose and J.E. Yukich (2002). Limit theory for random sequential packing and deposition. Ann. Appl. Probab. 12, 272-301.
    • (2002) Ann. Appl. Probab , vol.12 , pp. 272-301
    • Penrose, M.D.1    Yukich, J.E.2
  • 23
    • 0037274513 scopus 로고    scopus 로고
    • Weak laws of large numbers in geometric probability
    • M.D. Penrose and J.E. Yukich (2003). Weak laws of large numbers in geometric probability. Ann. Appl. Probab., 13, 277-303.
    • (2003) Ann. Appl. Probab. , vol.13 , pp. 277-303
    • Penrose, M.D.1    Yukich, J.E.2
  • 24
    • 85136400913 scopus 로고    scopus 로고
    • Normal approximation in geometric probability
    • eds. A.D. Barbour and Louis H.Y. Chen, Lecture Notes Series, Institute for Mathematical Sciences, World Scientific, Singapore. Also at arXiv:math.PR/0409088
    • M.D. Penrose and J.E. Yukich (2005). Normal approximation in geometric probability. In Stein's Method and Applications, eds. A.D. Barbour and Louis H.Y. Chen, Lecture Notes Series, Institute for Mathematical Sciences, Vol. 5, pp. 37-58. World Scientific, Singapore. Also at arXiv:math.PR/0409088
    • (2005) Stein's Method and Applications , vol.5 , pp. 37-58
    • Penrose, M.D.1    Yukich, J.E.2
  • 25
    • 21244487535 scopus 로고    scopus 로고
    • Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs
    • T. Schreiber, and J. E. Yukich (2005). Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs. Stochastic Process. Appl. 115, 1332-1356.
    • (2005) Stochastic Process. Appl. , vol.115 , pp. 1332-1356
    • Schreiber, T.1    Yukich, J.E.2
  • 27
    • 34547700829 scopus 로고    scopus 로고
    • Explicit laws of large numbers for random nearest-neighbour type graphs
    • to appear
    • Wade, A.R. (2007) Explicit laws of large numbers for random nearest-neighbour type graphs. Adv. Appl. Probab. 39, to appear.
    • (2007) Adv. Appl. Probab. , vol.39
    • Wade, A.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.