Lecture Notes in Mathematics

On the Estimation of Multiple Random Integrals and U-Statistics

Authors: Major, Peter

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About this book

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 linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables.
This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.

Table of contents (18 chapters)

  • Introduction

    Major, Péter

    Pages 1-3

  • Motivation of the Investigation: Discussion of Some Problems

    Major, Péter

    Pages 5-13

  • Some Estimates About Sums of Independent Random Variables

    Major, Péter

    Pages 15-20

  • On the Supremum of a Nice Class of Partial Sums

    Major, Péter

    Pages 21-33

  • Vapnik–Červonenkis Classes and L 2-Dense Classes of Functions

    Major, Péter

    Pages 35-39

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-37617-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-642-37616-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
On the Estimation of Multiple Random Integrals and U-Statistics
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2079
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-37617-7
DOI
10.1007/978-3-642-37617-7
Softcover ISBN
978-3-642-37616-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 288
Number of Illustrations and Tables
11 b/w illustrations
Topics