On the estimation of multiple random integrals and U-statistics
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...
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| Materialtyp: | Livre numérique |
| Språk: | Anglais |
| Publicerad: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Upplaga: | 1st ed. 2013. |
| Serie: | Lecture Notes in Mathematics
2079 |
| Ämnen: | |
| Länkar: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmärkning: |
L'impression du document génère 290 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • On the estimation of multiple random integrals and U-statistics, Péter Major, Berlin, Springer, 2013, 1 vol. (XIII-288 p.), Lecture notes in mathematics, 978-3-642-37616-0 • On the Estimation of Multiple Random Integrals and U-Statistics, Texte imprimé, 9783642376184 • On the estimation of multiple random integrals and U-statistics, Péter Major, Berlin, Springer, 2013, 1 vol. (XIII-288 p.), Lecture notes in mathematics, 978-3-642-37616-0 |
Innehållsförteckning:
- 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