| 书目名称 | Limit Theorems for Unions of Random Closed Sets | | 编辑 | Ilya S. Molchanov | | 视频video | | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | 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 ofrandomsets constructed similarly to the well-known distancesbetween distributions of random variables. The techniquesinclude regularly varying functions, topological propertiesof the space of closed sets, Choquetcapacities, convexanalysis and multivalued functions.Moreover, theconcept of regular variation is elaborated formultivalued (set-valued) functions. Applications of thelimit theorems to simulation of random sets, statisticaltests, polygonal approximations of compacts, limittheoremsfor 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 boo | | 出版日期 | Book 1993 | | 关键词 | Random variable; addition; random function; random set; regular variation; set-valued analysis; spatial st | | 版次 | 1 | | doi | https://doi.org/10.1007/BFb0073527 | | isbn_softcover | 978-3-540-57393-7 | | isbn_ebook | 978-3-540-48111-9Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 1993 |
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发表于 2025-3-21 16:05:00
