On the Estimation of Multiple Random Integrals and U-Statistics: 2079 (Lecture Notes in Mathematics, 2079) - Softcover

Major, Péter

 
9783642376160: On the Estimation of Multiple Random Integrals and U-Statistics: 2079 (Lecture Notes in Mathematics, 2079)
Softcover
ISBN 10: 3642376169 ISBN 13: 9783642376160
Publisher: Springer, 2013

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2013
Language
English
ISBN 10 
3642376169
ISBN 13 
9783642376160
Binding
Paperback
Number of pages
301

Other Popular Editions of the Same Title

9783642376184: On the Estimation of Multiple Random Integrals and U-Statistics

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ISBN 10:  3642376185 ISBN 13:  9783642376184
Publisher: Springer, 2013
Softcover