Geometric Aspects of Probability Theory and Mathematical Statistics

ISBN-13: 9789048155057 / Angielski / Miękka / 2010 / 304 str.

V. V. Buldygin; A. B. Kharazishvili

Opis

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.

Spis treści

Preface. 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. Appendices. Bibliography. Subject Index.