Limit Theorems for Unions of Random Closed Sets

Molchanov, Ilya S.

ISBN 10: 3540573933 / ISBN 13: 9783540573937

Published by Springer, 1993

About this Item

This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,300grams, ISBN:3540573933.

Seller Inventory # 2932997

Bibliographic Details

• Title: Limit Theorems for Unions of Random Closed Sets
• Publisher: Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 3540573933
• ISBN 13: 9783540573937
• Binding: Soft cover
• Condition: Good
• Weight: 300 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed.