INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783642376177
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52321
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
On the Estimation of Multiple Random Integrals and U-Statistic
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by P?شter Major
fa
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Berlin, Heidelberg
Name of Publisher, Distributor, etc.
: Springer Berlin Heidelberg :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XIII, 288 p. 11 illus., online resource.
SERIES
Series Title
(Lecture Notes in Mathematics,0075-8434
Volume Designation
; 2079)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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.
Text of Note
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- ??ervonenkis classes and L2-dense 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 U-statistics -- 10 MultipleWiener-It?لإ integrals and their properties -- 11 The diagram formula for products of degenerate U-statistics -- 12 The proof of the diagram formula for U-statistics -- 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.?╗╣
SERIES
Title
Lecture Notes in Mathematics,0075-8434
Volume Number
2079
TOPICAL NAME USED AS SUBJECT
Mathematics
Distribution (Probability theory)
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Major, P?شter.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783642376160.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783642376160.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
