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Limit Theorems for Unions of Random Closed Sets

Limit Theorems for Unions of Random Closed Sets (Paperback)

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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.

Science & MathematicsMathematicsAlgebraScience & MathematicsMathematicsMathematical foundationsSet theory Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 29/11/1993 ISBN-13: 9783540573937  Details: Type: Paperback Format: Books
Availability: Printed to order. Despatched in 2-3 weeks.  

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