On the Estimation of Multiple Random Integrals and U-Statistics

This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linea...

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Bibliographic Details
Main Author Major, Péter
Format eBook Book
LanguageEnglish
Published Berlin, Heidelberg Springer Nature 2013
Springer
Springer Berlin / Heidelberg
Springer Berlin Heidelberg
Edition1
SeriesLecture Notes in Mathematics
Subjects
Distribution (Probability theory)
Mathematics
Mathematics and Statistics
Probabilities & applied mathematics
Probability Theory and Stochastic Processes
Stochastic integrals
Stochastic processes
U-statistics
Online AccessGet full text
ISBN9783642376177
3642376177
3642376169
9783642376160
ISSN0075-8434
1617-9692
DOI10.1007/978-3-642-37617-7

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Table of Contents:
  • Intro -- Preface -- Contents -- Acronyms -- Chapter 1 Introduction -- Chapter 2 Motivation of the Investigation: Discussion of Some Problems -- Chapter 3 Some Estimates About Sums of Independent Random Variables -- Chapter 4 On the Supremum of a Nice Class of Partial Sums -- Chapter 5 Vapnik-Červonenkis Classes and L2-Dense Classes of Functions -- Chapter 6 The Proof of Theorems 4.1 and 4.2 on the Supremum of Random Sums -- Chapter 7 The Completion of the Proof of Theorem 4.1 -- Chapter 8 Formulation of the Main Results of This Work -- Chapter 9 Some Results About U-statistics -- Chapter 10 Multiple Wiener-Itô Integrals and Their Properties -- Chapter 11 The Diagram Formula for Products of Degenerate U-Statistics -- Chapter 12 The Proof of the Diagram Formula for U-Statistics -- Chapter 13 The Proof of Theorems 8.3, 8.5 and Example 8.7 -- Chapter 14 Reduction of the Main Result in This Work -- Chapter 15 The Strategy of the Proof for the Main Result of This Work -- Chapter 16 A Symmetrization Argument -- Chapter 17 The Proof of the Main Result -- Chapter 18 An Overview of the Results and a Discussion of the Literature -- Appendix A The Proof of Some Results About Vapnik-Červonenkis Classes -- Appendix B The Proof of the Diagram Formula for Wiener-Itô Integrals -- Appendix C The Proof of Some Results About Wiener-Itô Integrals -- Appendix D The Proof of Theorem 14.3 About U-Statistics and Decoupled U-Statistics -- References -- Index