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Limit Theorems for Unions of Random Closed Sets: Lecture Notes in Mathematics, cartea 1561

Autor Ilya S. Molchanov
en Limba Engleză Paperback – 29 noi 1993
The book concerns limit theorems and laws of large numbersfor scaled unionsof independent identically distributedrandom sets. These results generalizewell-known facts fromthe theory of extreme values. Limiting distributions (calledunion-stable) are characterized and found explicitly formany examples of random closed sets. The speed ofconvergence in the limit theorems for unions is estimated bymeans of the probability metrics method.It includes theevaluation of distances between distributions of randomsets constructed similarly to the well-known distancesbetween distributions of random variables. The techniquesinclude regularly varying functions, topological propertiesof the space of closed sets, Choquet capacities, convexanalysis and multivalued functions.Moreover, the concept of regular variation is elaborated formultivalued (set-valued) functions. Applications of thelimit theorems to simulation of random sets, statisticaltests, polygonal approximations of compacts, limit theoremsfor pointwise maxima of random functions are considered.Several open problems are mentioned.Addressed primarily to researchers in the theory of randomsets, stochastic geometry and extreme value theory, the bookwill also be of interest to applied mathematicians workingon applications of extremal processes and their spatialcounterparts. The book is self-contained, and no familiaritywith the theory of random sets is assumed.
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Specificații

ISBN-13: 9783540573937
ISBN-10: 3540573933
Pagini: 168
Ilustrații: X, 158 p.
Dimensiuni: 156 x 234 x 9 mm
Greutate: 0.25 kg
Ediția:1993
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

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Research

Cuprins

Distributions of random closed sets.- Survey on stability of random sets and limit theorems for Minkowski addition.- Infinite divisibility and stability of random sets with respect to unions.- Limit theorems for normalized unions of random closed sets.- Almost sure convergence of unions of random closed sets.- Multivalued regularly varying functions and their applications to limit theorems for unions of random sets.- Probability metrics in the space of random sets distributions.- Applications of limit theorems.