Theory of Random Sets

• Main Author: Molchanov, Ilya (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Probability Theory and Stochastic Modelling, 87
• Subjects: Mathematics.; Game theory.; Probabilities.; Physics.; Statistics.; Electrical engineering.; Economic theory.; Probability Theory and Stochastic Processes.; Game Theory, Economics, Social and Behav. Sciences.; Theoretical, Mathematical and Computational Physics.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.; Electrical Engineering.; Economic Theory/Quantitative Economics/Mathematical Methods.

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the fou...

Table of Contents:

• 1 Random Closed Sets and Capacity Functionals
• 2 Expectations of Random Sets
• 3 Minkowski Sums
• 4 Unions of Random Sets
• 5 Random Sets and Random Functions
• A Topological spaces and metric spaces
• B Linear spaces
• C Space of closed sets
• D Compact sets and the Hausdorff metric
• E Multifunctions and semicontinuity
• F Measures and probabilities
• G Capacities
• H Convex sets
• I Semigroups, cones, and harmonic analysis
• J Regular variation
• References.