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Geometric aspects of probability theory and mathematical statistics /

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This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questio...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Buldygin, V. V. (Valeriĭ Vladimirovich), Kharazishvili, A. B.
Format: eBook
Language:English
Published: Dordrecht ; Boston : Kluwer Academic, [2000]
Series:Mathematics and its applications (Kluwer Academic Publishers) ; volume 514.
Subjects:
Geometric probabilities.
Convex domains.
Probabilidade.
Estruturas algébricas e topológicas.
Probabilidade geométrica.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Convex sets in vector spaces
  • 2. Brunn-Minkowski inequality
  • 3. Convex polyhedra
  • 4. Two classical isoperimetric problems
  • 5. Some infinite-dimensional vector spaces
  • 6. Probability measures and random elements
  • 7. Convergence of random elements
  • 8. The structure of supports of Borel measures
  • 9. Quasi-invariant probability measures
  • 10. Anderson inequality and unimodal distributions
  • 11. Oscillation phenomena and extensions of measures
  • 12. Comparison principles for Gaussian processes
  • 13. Integration of vector-valued functions and optimal estimation of stochastic processes
  • App. 1. Some properties of convex curves
  • App. 2. Convex sets and number theory
  • App. 3. Measurability of cardinals.