On the Estimation of Multiple Random Integrals and U-Statistics

Péter Major

ISBN 10: 3642376169 / ISBN 13: 9783642376160

Editore: Springer Berlin Heidelberg, 2013

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Druck auf Anfrage Neuware - Printed after ordering - 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 linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables.This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.

Codice articolo 9783642376160

Dati bibliografici

• Titolo: On the Estimation of Multiple Random Integrals and U-Statistics
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3642376169
• ISBN 13: 9783642376160
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 17 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 17 millimetri di profondità
• Peso: 464 grammi

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Riassunto

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 linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables.
This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.