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

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Author/Creator:
Major, Péter, 1947-
Language:
English.
Publication date:
2013
Copyright date:
2013
Publication:
Heidelberg ; New York : Springer, [2013]
Copyright notice:
©2013
Format:
  • Book
  • xiii, 288 pages ; 24 cm.
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-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.
Available in another form:
Online version: Major, Péter, 1947- On the estimation of multiple random integrals and u-statistics. Berlin : Springer, c2013 3642376177 (OCoLC)851400422
Series:
Lecture notes in mathematics, 1617-9692 ; 2079
Lecture notes in mathematics (Springer-Verlag) ; 2079.
Subjects:
ISBN:
3642376169
9783642376160

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