Limit Theorems for Unions of Random Closed Sets

ISBN-13: 9783540573937 / Angielski / Miękka / 1993 / 158 str.

Ilya S. Molchanov

Opis

This monograph examines limit theorems and the laws of large numbers for scaled unions of independent, identically-distributed random sets. The results generalize well-known facts about the theory of extreme values. Limiting distributions are characterized and found for random closed sets.

Spis treści

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.