Molchanov I.I. — Limit theorems for unions of random closed sets :: Электронная библиотека попечительского совета мехмата МГУ

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Molchanov I.I. — Limit theorems for unions of random closed sets

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Название: Limit theorems for unions of random closed sets

Автор: Molchanov I.I.

Аннотация:

The book begins with the introduction of the basic tools and known results on random sets distributions and their weak convergence. Although the book is devoted to the study of limit theorems for unions. in Chapter 2 we present several results on Minkowski sums of random compact sets in the Euclidean space. In Chapter 3 we bring the notions of union stable and convex stable random closed sets. Their distributions are characterized in terms of the corresponding capacity or inclusion functionals. In Chapter 4 of 8 we prove limit theorems for scaled unions and convex hulls of random sets. Limit theorems for unions of special random sets and et cetera.

Язык:

Рубрика: Математика/Вероятность/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 165

Добавлена в каталог: 05.06.2005

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Предметный указатель

$\mathbb{F}$ -addition      23
$\mathbb{F}$ -closed set      20
$\mathbb{F}$ -expectation of a random set      19
$\mathcal{F}$ -convergence      2
Addition-scheme      15
Alternating Choquet capacity      3
Alternating Choquet capacity of in nite order      30
Ambarzumian, R.V.      147
Approximation of convex sets      38 139
Araujo, A.      17 147
Arrow, K.J.      17 147
Artstein, Z.      15 16 85 147
Asymptotic inverse function      13 56
Attouch, H.      134 147
Aubin, J.-P.      85 147
Aumann, R.      15 147
Baddeley, A.J.      103 112 147
Balkema, A.A.      30 41 147
Ball      1
Berg, C.      30 147
Bhattacharia, R.N.      26 147
Billingsley, P.      10 147
Boolean model      35
Boolean model as U-stable set      36
Boolean model, simulation      123
Borel — Cantelli lemma      72
Boundary of a set      2
C-stable random set      see Convex-stable random set
Canonically closed set      2
Capacity functional      3
Capacity integral      18
Capacity, homogeneous      30 45 109
Capacity, maxitive      see Maxitive capacity
Capacity, regularly varying      69
Castaign representation      102
Cauchy distribution      60 119
Central limit theorem for random sets      17
Choquet capacity      3
Choquet theorem      3
Choquet, G.      6 36 147
Christensen, J.P.R.      30 147
Clarke, H.      85 147
Closure of a set      2
Compacti cation      5
Complement      2
Cone      59
Cone, canonically closed      86
Continuity set      7
Convergence of capacities, pointwise      48 49
Convergence of capacities, uniform      49
Convergence of closed sets      1
Convergence of compact sets      2
Convex hull      2
Convex random set      5
Convex-stable random set      38
Convex-stable random set of the first type      41
Convex-stable random set of the second type      41
Corrosion propagation      129
Cressie, N.A.C.      1 17 147
Davis, R.A.      38 67 68 71 74—76 79 82 127 148
Density regularly varying      55
Disease propagation      127
Dudley, R.M.      27 148
Ekeland, I.      85 147
Engineering metric      102
Envelope of a set      2
Epi-convergence      140
Epigraph      139
Equilibrium measure      37
Euclidean metric      1
Euclidean norm      1
Euclidean space      1
Expectation of a random set      11 15
Exponent of a regularly varying function      13
Exponent of a regularly varying function, multivariate      14
Feller, W.      13 148
Fixed point      29
Frankowska, H.      85 147
Function, asymptotic inverse      13
Function, multivalued      86
Function, regularly varying      46
Function, upper semi-continuous      134
Functional, homogeneous      111
Functional, strictly monotone      70
Galambos, J.      30 38 41 45 49 50 53 148
Gaussian random sample      130
Gaussian random set      17
Gerritse B.      18 148
Gerritse, G.      65 148
Gine, E.      15 17 18 30 38 40 41 147 148
Groeneboom, P.      139 148
Haan, L. de      13 14 30 77 95 148
Hahn, F.H.      17 147
Hahn, M.      15 17 18 38 148
Hausdor metric      2
Hengartner, W.      106 108 148
Hiai, F.      15 85 148 149
Hitting functional      3
Homogeneous capacity      30 45 109
Homogeneous function      14
Homogeneous metric      102 110
Huber, P.      18 149
Hypo-convergence      134
Hypograph      134
Ideal metric      110
Inclusion functional      6 38 51
Index of a regularly varying function      13
Index of a regularly varying function, multivalued      86
Index of a regularly varying function, multivariate      14
Intensity measure      35
Interior of a set      2
Inverse function      91
Inversion of a set      34
Ito, K.      149
K-convergence      2
Kalashnikov, V.V.      101 149
Kendall, D.G.      1 3 149 151
Kernel      36
Khinchin lemma      43 44 65
Kruse, R.      16 149
Landkof, N.C.      36 37 111 149
Laslett, G.M.      1 147
Law of large numbers for Minkowski sums      16
Law of large numbers for unions      71
Leadbetter, M.R.      30 43 149
Lebesgue measure      11 16
Lebesgue measure on the sphere      58
Levy metric for random sets      103
Levy metric for random variables      107
Levy — Prokhorov metric      101

Lindgren, G.      149
Lyashenko, N.N.      4 7 8 17 138 149
Markov inequality      130
Matheron, G.      1 3 12 18—20 22 29—31 35 37 57 67 69 73 108 111 123 132 149
Max-stable distribution      30
Max-stable random process      30
Max-stable random variable      30
Max-stable random vector      30 41
Maximum principle      36
Maxitive capacity      4 36
McClure, D.E.      139 149
McKean, H.P.      149
Mecke, J.      1 151
Minitive capacity      70
Minkowski addition      2 12
Minkowski functionals      108
Minkowski subtraction      12
Molchanov, I.S.      4 5 8 16 26 27 31 71 85 134 149 150
Monotone capacity of infinite order      6
Mulrow, E.      67 127 148
Multivalued function      85
Multivalued function, convex-valued      88
Multivalued function, homogeneous      115
Multivalued function, regularly varying      86
Multivariate regularly varying function      14
Newton capacity      111
Norberg, T.      1 4 8 18 30 65 70 99 134 135 138 150
Norm of a set      12 15
Omey, E.      14 148
Outer normal vector      139
Pancheva, E.      65 150
Papageorgiou, N.S.      85 150
Poisson point process      35 57
Poisson point process, stationary      35
Polygonal approximation      139
Polyhedron random      139
Probability metric      101
Probability metric, homogeneous      102 110
Probability metric, ideal      110
Probability metric, regular      110
Probability metric, semi-homogeneous      118
Probability metrics method      101
Puri, M.L.      15 150
Rachev, S.T.      101 103 149 150
Ralescu, D.A.      15 150
Random ball      84 85
Random closed set      2
Random closed set, additive U-stable      43
Random closed set, compact      5
Random closed set, convex      5
Random closed set, convex-stable      38
Random closed set, generalized U-stable      42
Random closed set, homogeneous at infinity      43
Random closed set, inverted U-stable      44
Random closed set, isotropic      5
Random closed set, non-trivial      29
Random closed set, simulation      124
Random closed set, stationary      5
Random closed set, strictly C-stable      38
Random closed set, U-stable      30
Random closed set, union stable      30
Random closed set, union-in nitely-divisible      29
Random constraints      144
Random half-space      142
Random sample      67
Random set, Gaussian      17
Random set, p-stable      18
Random triangle      125
Random variable max-stable      30
Random vector max-stable      30 41
Ranga Rao, R.      26 147
Regular metric      110
Regularly varying function      13
Regularly varying function at zero      49
Regularly varying function index      13
Resnick, S.I.      14 30 41 67 74 76 77 95 127 147 148 150
Ressel, P.      30 147
Riesz capacity      37
Robbins formula      123 132
Robbins, H.E.      123 150
Rockafellar, R.T.      85 91 150
Rootzen, H.      149
Rose of directions      128
Salinetti, G.      4 7 8 85 134 135 140 150 151
Santalo, L.A.      131 151
Schneider, R.      38 129 139 151
Selector      22 102
Semi-homogeneous metric      117
Seneta, E.      13 46 56 69 89 151
Serra, J.      12 123 151
Set-valued function      85
Shapley — Folkmann lemma      17
Space of closed sets      1
Stable random process      37
Standard class      105
Star-cluster      38 127
Steiner formula      108
Stoyan, D.      1 11 12 16 18 20 24 35 108 123 151
Stoyan, H.      16 18 151
Support function      7 12
Theodorescu, R.      106 108 148
Tomkins, R.      74 76 150
Total variation distance      108
Trader, D.A.      5 29 40 43 151
Umegaki, H.      85 149
Uniform for random variables      103
Uniform metric for random sets      103
union      11
Union-scheme      45
Union-stable random set      30 109
Union-stable random set, simulation      124
Unit sphere      9
Upper limit in $\mathcal{F}$       2
Upper limit in $\mathcal{K}$       2
Upper semi-continuous function      5
Upper semi-continuous functional      3
Uryson, P.S.      131 151
Variance of a random set      16
Vatan, P.      38 148
Vervaat, W.      1 150 151
Vitale, R.A.      5 11 15—18 22 57 130 139 147 149 151
Volume of random samples      129
Wagner, D.      151
Weak convergence of random sets      7 104
Weak convergence, determine class      8
Weak convergence, determining class      104
Weil, W.      17 26 151
Wets, R.J.-B.      4 7 8 85 91 134 135 140 147 151
Yakimiv, A.L.      14 77 86 87 151
Zinn, J.      148
Zolotarev, V.M.      65 101—103 108 110 114 151 152

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