On the Estimation of Multiple Random Integrals and U-Statistics

By Peter Major

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- Červonenkis 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 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.

• Format: Paperback
• Language: English
• ISBN: 3642376169
• ISBN13: 9783642376160
• Release Date: July 2013
• Publisher: Springer
• Length: 288 Pages
• Weight: 0.95 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"