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On the estimation of multiple random integrals and U-statistics

Author: Péter Major
Publisher: Heidelberg ; New York : Springer, [2013] ©2013
Series: Lecture notes in mathematics (Springer-Verlag), 2079.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This work starts with the study of those limit theorems in probability theory for which classical methods do not work.

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Additional Physical Format: Online version:
Major, Péter, 1947-
On the estimation of multiple random integrals and u-statistics.
Berlin : Springer, ©2013
(OCoLC)851400422
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Péter Major
ISBN: 3642376169 9783642376160 3642376177 9783642376177
OCLC Number: 830367462
Description: xiii, 288 pages ; 24 cm
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-Ĉervonenkis 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 --
8. Formulation of the main results of this work --
9. Some results about U-statistics --
10. Multiple Wiener-Itô 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 --
A. The proof of some results about Vapnik-Ĉervonenkis classes --
B. The proof of the diagram formula for Wiener-Itô integrals --
C. The proof of some results about Wiener-Itô integrals --
D. The proof of theorem 14.3 about U-statistics and decoupled U-statistics.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2079.
Responsibility: Péter Major.

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