On the estimation of multiple random integrals and Ustatistics / Péter Major.
 Publication:
 Heidelberg ; New York : Springer, [2013]
 Series:
 Lecture notes in mathematics (SpringerVerlag) ; 2079.
Lecture notes in mathematics, 16179692 ; 2079  Format/Description:
 Book
xiii, 288 pages ; 24 cm.  Subjects:
 Ustatistics.
Stochastic processes.
Distribution (Probability theory).  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. VapnikĈervonenkis 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
8. Formulation of the main results of this work
9. Some results about Ustatistics
10. Multiple WienerItô 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
A. The proof of some results about VapnikĈervonenkis classes
B. The proof of the diagram formula for WienerItô integrals
C. The proof of some results about WienerItô integrals
D. The proof of theorem 14.3 about Ustatistics and decoupled Ustatistics.  Notes:
 Includes bibliographical references and index.
 ISBN:
 3642376169
9783642376160  OCLC:
 830367462

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