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Limit Theorems for Unions of Random Closed Sets (Paperback, 1993 ed.)
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Limit Theorems for Unions of Random Closed Sets (Paperback, 1993 ed.)
Series: Lecture Notes in Mathematics, 1561
Expected to ship within 10 - 15 working days
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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.
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