메뉴 건너뛰기




Volumn 31, Issue 2, 1999, Pages 283-314

Central limit theorem for a class of random measures associated with germ-grain models

Author keywords

Germ grain model; Intrinsic volumes; M dependent random field; Mixing Boolean model; Random measure; Random set; Weak dependence

Indexed keywords


EID: 0033141155     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1029955136     Document Type: Article
Times cited : (42)

References (36)
  • 1
    • 0012489605 scopus 로고
    • Alimit theoremfor statistics of spatial data
    • BADDELEY, A. J. (1980). Alimit theoremfor statistics of spatial data. Adv. Appl. Prob. 12, 447-461.
    • (1980) Adv. Appl. Prob , vol.12 , pp. 447-461
    • Baddeley, A.J.1
  • 2
    • 0343451517 scopus 로고
    • On second-orderformulas in anisotropic stereology
    • BENEŠ, V. (1995). On second-orderformulas in anisotropic stereology. Adv. Appl. Prob. 27, 326-343.
    • (1995) Adv. Appl. Prob , vol.27 , pp. 326-343
    • Beneš, V.1
  • 3
    • 84985370188 scopus 로고
    • On some characteristics of anisotropic fibre processes
    • BENEŠ, V., Chadœuf, J. and OHSER, J. (1994). On some characteristics of anisotropic fibre processes. Math. Nachr. 169,5-17.
    • (1994) Math. Nachr. , vol.169 , pp. 5-17
    • Beneš, V.1    Chadœuf, J.2    Ohser, J.3
  • 6
    • 0342581623 scopus 로고
    • M-dependent random fields with analytical cumulant generating function
    • GOTZE, F., HEINRICH, L. and Hipp, C. (1995). m-dependent random fields with analytical cumulant generating function. Scand. J. Statist. 22, 183-195.
    • (1995) Scand. J. Statist , vol.22 , pp. 183-195
    • Gotze, F.1    Heinrich, L.2    Hipp, C.3
  • 8
    • 0002828513 scopus 로고
    • On classes of random sets and point processes
    • HANISCH, K.-H. (1981). On classes of random sets and point processes. Serdica 7,160-166.
    • (1981) Serdica , vol.7 , pp. 160-166
    • Hanisch, K.-H.1
  • 9
    • 84985425941 scopus 로고
    • Asymptotic behaviour of an empirical nearest-neighbour distance function for stationary Poisson cluster process
    • HEINRICH, L. (1988). Asymptotic behaviour of an empirical nearest-neighbour distance function for stationary Poisson cluster process. Math. Nachr 136,131-148.
    • (1988) Math. Nachr , vol.136 , pp. 131-148
    • Heinrich, L.1
  • 10
    • 84953477234 scopus 로고
    • Asymptotic Gaussianity of some estimators for reduced factorial moment measures and product densities of stationary Poisson cluster processes
    • HEINRICH, L. (1988). Asymptotic Gaussianity of some estimators for reduced factorial moment measures and product densities of stationary Poisson cluster processes. Statistics 19, 87-106.
    • (1988) Statistics , vol.19 , pp. 87-106
    • Heinrich, L.1
  • 11
    • 0002359086 scopus 로고
    • On existence and mixing properties of germ-grain models
    • HEINRICH, L. (1992). On existence and mixing properties of germ-grain models. Statistics 23, 271-286.
    • (1992) Statistics , vol.23 , pp. 271-286
    • Heinrich, L.1
  • 12
    • 0343887317 scopus 로고
    • Asymptoticproperties of minimumcontrastestimators forparameters of Booleanmodels
    • HEINRICH, L. (1993). Asymptoticproperties of minimumcontrastestimators forparameters of Booleanmodels. Metrika 31,349-360.
    • (1993) Metrika , vol.31 , pp. 349-360
    • Heinrich, L.1
  • 13
    • 0007420038 scopus 로고
    • Normal approximationfor some mean-value estimates of absolutelyregulartessellations
    • HEINRICH, L. (1994). Normal approximationfor some mean-value estimates of absolutelyregulartessellations. Math. Meth. Statist. 3,1-24.
    • (1994) Math. Meth. Statist , vol.3 , pp. 1-24
    • Heinrich, L.1
  • 14
    • 0010080917 scopus 로고
    • Central limit theorems for point processes. Stochast. Process
    • IVANOFF, B. G. (1982). Central limit theorems for point processes. Stochast. Process. Appl. 12,171-186.
    • (1982) Appl , vol.12 , pp. 171-186
    • Ivanoff, B.G.1
  • 15
    • 0040599263 scopus 로고
    • Central limit theorem and convergence of empirical processes for stationary point processes
    • P. Bartfai and J. Tomko. North-Holland, Amsterdam
    • JOLIVET, E. (1982). Central limit theorem and convergence of empirical processes for stationary point processes. In Point Processes and Queuing Problems, eds. P. Bartfai and J. Tomko. North-Holland, Amsterdam, pp. 117-161.
    • (1982) Point Processes and Queuing Problems , pp. 117-161
    • Jolivet, E.1
  • 16
    • 73249151825 scopus 로고
    • 3rd edn. Academic Press, New York
    • KALLENBERG, O. (1983). RandomMeasures, 3rd edn. Academic Press, New York.
    • (1983) Randommeasures
    • Kallenberg, O.1
  • 17
    • 0037708521 scopus 로고
    • Asymptotic properties of stereological estimators of volume fraction for stationary random sets
    • Mase, S. (1982). Asymptotic properties of stereological estimators of volume fraction for stationary random sets. J. Appl. Prob. 19,111-126.
    • (1982) J. Appl. Prob , vol.19 , pp. 111-126
    • Mase, S.1
  • 18
    • 0343451503 scopus 로고
    • Properties of fourth-order, strong mixing rates and its application to random set theory
    • Mase, S. (1982). Properties of fourth-order, strong mixing rates and its application to random set theory. J. Multivariate Anal. 12, 549-561.
    • (1982) J. Multivariate Anal , vol.12 , pp. 549-561
    • Mase, S.1
  • 20
    • 0001871767 scopus 로고
    • Statistics of the Boolean model: From the estimation of means to the estimation of distributions
    • MOLCHANOV, I. S. (1995). Statistics of the Boolean model: from the estimation of means to the estimation of distributions. Adv. Appl. Prob. 27, 63-86.
    • (1995) Adv. Appl. Prob , vol.27 , pp. 63-86
    • Molchanov, I.S.1
  • 22
    • 0000594254 scopus 로고
    • Asymptotic properties of estimators for parameters of the Boolean model
    • MOLCHANOV, I. S. and STOYAN, D. (1994). Asymptotic properties of estimators for parameters of the Boolean model. Adv. Appl. Prob. 26, 301-323.
    • (1994) Adv. Appl. Prob , vol.26 , pp. 301-323
    • Molchanov, I.S.1    Stoyan, D.2
  • 23
    • 0039586300 scopus 로고
    • Ergodic theorems for spatial processes. Z
    • NGUYEN, X. X. and Zessin, H. (1979). Ergodic theorems for spatial processes. Z. Wahrscheinlichkeitsth. 48, 133-158.
    • (1979) Wahrscheinlichkeitsth , vol.48 , pp. 133-158
    • Nguyen, X.X.1    Zessin, H.2
  • 24
    • 0000844336 scopus 로고
    • Parallelmengen mit Vielfachheit und Steiner-Formeln. Geom
    • SCHNEIDER, R. (1980). Parallelmengen mit Vielfachheit und Steiner-Formeln. Geom. Dedicata 2, 111-127.
    • (1980) Dedicata , vol.2 , pp. 111-127
    • Schneider, R.1
  • 28
    • 84986716171 scopus 로고
    • An alternate formulation of mean value for random geometric figures
    • VITALE, R. A. (1988). An alternate formulation of mean value for random geometric figures. J. Microscopy 151,197-204.
    • (1988) J. Microscopy , vol.151 , pp. 197-204
    • Vitale, R.A.1
  • 29
    • 0000753060 scopus 로고
    • Somelimit theorems forrandomfunctions
    • VOLKONSKII, V. A. and Rozanov, Yu. A. (1959). Somelimit theorems forrandomfunctions. Theory Prob. Appl. 4, 178-197.
    • (1959) Theory Prob. Appl , vol.4 , pp. 178-197
    • Volkonskii, V.A.1    Rozanov, Y.A.2
  • 30
    • 0038292315 scopus 로고
    • Stereology: A survey for geometers
    • P. M. Gruber and J. M. Wills. Birkhauser, Basel
    • WEIL, W. (1983). Stereology: a survey for geometers. In Convexity and Its Applications, ed. P. M. Gruber and J. M. Wills. Birkhauser, Basel, pp 360-412.
    • (1983) Convexity and Its Applications , pp. 360-412
    • Weil, W.1
  • 31
    • 84986703405 scopus 로고
    • Expectation formulas and isoperimetric properties for non-isotropic Boolean models
    • WEIL, W. (1988). Expectation formulas and isoperimetric properties for non-isotropic Boolean models. J. Microscopy 151, 235-245.
    • (1988) J. Microscopy , vol.151 , pp. 235-245
    • Weil, W.1
  • 32
    • 0011303556 scopus 로고
    • The estimation of mean shape and mean particle number in overlapping particle systems in the plane
    • WEIL, W. (1995). The estimation of mean shape and mean particle number in overlapping particle systems in the plane. Adv. Appl. Prob. 27, 102-119.
    • (1995) Adv. Appl. Prob , vol.27 , pp. 102-119
    • Weil, W.1
  • 33
    • 0000220346 scopus 로고
    • Densities for stationary random sets and point processes
    • WEIL, W. and Wieacker, J. A. (1984). Densities for stationary random sets and point processes. Adv. Appl. Prob. 16, 324-346.
    • (1984) Adv. Appl. Prob , vol.16 , pp. 324-346
    • Weil, W.1    Wieacker, J.A.2
  • 34
    • 0040220600 scopus 로고
    • Limiting behavior of U-statistics for stationary absolutely regular processes
    • YOSHIHARA, K.-I. (1976). Limiting behavior of U-statistics for stationary absolutely regular processes. Z. Wahrscheinlichkeitsth. 35, 237-252.
    • (1976) Z. Wahrscheinlichkeitsth , vol.35 , pp. 237-252
    • Yoshihara, K.-I.1
  • 35
    • 0002222913 scopus 로고
    • Random processes of Hausdorff rectifiable closed sets
    • Zähle, M. (1982). Random processes of Hausdorff rectifiable closed sets. Math. Nachr. 108, 49-72.
    • (1982) Math. Nachr , vol.108 , pp. 49-72
    • Zähle, M.1
  • 36
    • 0039411057 scopus 로고
    • Curvature measures and random sets, II
    • Zähle, M. (1986). Curvature measures and random sets, II. Prob. Theory Rel. Fields 71, 37-58.
    • (1986) Prob. Theory Rel. Fields , vol.71 , pp. 37-58
    • Zähle, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.