On the Estimation of Multiple Random Integrals and U-Statistics

• Κύριος συγγραφέας: Major, Péter (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Σειρά: Lecture Notes in Mathematics, 2079
• Θέματα: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.

This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linea...

Πίνακας περιεχομένων:

• 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–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.