Overview

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 questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are 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:   Softcover reprint of hardcover 1st ed. 2000
Volume:   514
Dimensions:   Width: 21.00cm , Height: 1.60cm , Length: 27.90cm
Weight:   0.781kg
ISBN:  

9789048155057

ISBN 10:   9048155053
Pages:   304
Publication Date:   09 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

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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