Franklin

On the estimation of multiple random integrals and U-statistics / Péter Major.

Author/Creator:
Major, Péter, 1947-
Publication:
Heidelberg ; New York : Springer, [2013]
Series:
Lecture notes in mathematics (Springer-Verlag) ; 2079.
Lecture notes in mathematics, 1617-9692 ; 2079
Format/Description:
Book
xiii, 288 pages ; 24 cm.
Subjects:
U-statistics.
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. 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.
Notes:
Includes bibliographical references and index.
ISBN:
3642376169
9783642376160
OCLC:
830367462
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