Overview

This text demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The text is essentially self-contained, and the presentation of material is thorough in detail. The topics considered in the text should be accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.

Full Product Details

Author:   V.V. Buldygin ,  A.B. Kharazishvili
Publisher:   Springer
Imprint:   Springer
Edition:   2000 ed.
Volume:   514
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   1.370kg
ISBN:  

9780792364139

ISBN 10:   0792364139
Pages:   304
Publication Date:   31 August 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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.- Appendix 1: Some properties of convex curves.- Appendix 2: Convex sets and number theory.- Appendix 3: Measurability of cardinals.

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