On the estimation of multiple random integrals and Ustatistics
 Responsibility
 Péter Major.
 Language
 English.
 Publication
 Heidelberg ; New York : Springer, [2013]
 Copyright notice
 ©2013
 Physical description
 xiii, 288 pages ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2079.
Access
Creators/Contributors
 Author/Creator
 Major, Péter, 1947
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 1 Introduction. 2 Motivation of the investigation. Discussion of some problems. 3 Some estimates about sums of independent random variables. 4 On the supremum of a nice class of partial sums. 5 Vapnik Cervonenkis classes and L2dense classes of functions . 6 The proof of Theorems 4.1 and 4.2 on the supremum of random sums. 7 The completion of the proof of Theorem 4.1. 8 Formulation of the main results of this work. 9 Some results about Ustatistics. 10 MultipleWienerIto integrals and their properties. 11 The diagram formula for products of degenerate Ustatistics. 12 The proof of the diagram formula for Ustatistics. 13 The proof of Theorems 8.3, 8.5 and Example 8.7. 14 Reduction of the main result in this work. 15 The strategy of the proof for the main result of this work. 16 A symmetrization argument. 17 The proof of the main result. 18 An overview of the results and a discussion of the literature.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 socalled degenerate Ustatistics 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 nonlinear 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.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Series
 Lecture notes in mathematics, 16179692 ; 2079
 Available in another form
 Online version: Major, Péter, 1947 On the estimation of multiple random integrals and ustatistics. Berlin : Springer, c2013 3642376177 (OCoLC)851400422
 ISBN
 3642376169
 9783642376160