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Geometric and nonlinear limit theore...

Fresen, Daniel John.

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Geometric and nonlinear limit theorems in probability theory.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometric and nonlinear limit theorems in probability theory./
Author:	Fresen, Daniel John.
Description:	98 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-03(E), Section: B.
Contained By:	Dissertation Abstracts International74-03B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3530878
ISBN:	9781267708939

Geometric and nonlinear limit theorems in probability theory.
Fresen, Daniel John.

Geometric and nonlinear limit theorems in probability theory. - 98 p.

Source: Dissertation Abstracts International, Volume: 74-03(E), Section: B.

Thesis (Ph.D.)--University of Missouri - Columbia, 2012.

The concentration of measure phenomenon is a nonlinear equivalent of the law of large numbers that deals with real valued Lipschitz functions and includes linear functionals such as the sample mean. In the first part of this dissertation we study functions that take values in more general metric-like spaces and have the property that they are invariant under coordinate permutations. In Chapter 1 we study functions that take values in the space of convex bodies, in Chapter 2 we study order statistics and in Chapter 3 we prove abstract concentration inequalities for functions taking values in an arbitrary metric space.

ISBN: 9781267708939Subjects--Topical Terms:

515831
Mathematics.

Geometric and nonlinear limit theorems in probability theory.
LDR:02041nam a2200313 4500 001 1963029
005 20140924121923.5
008 150210s2012 ||||||||||||||||| ||eng d
020 $a 9781267708939
035 $a (MiAaPQ)AAI3530878
035 $a AAI3530878
040 $a MiAaPQ $c MiAaPQ
100 1 $a Fresen, Daniel John. $3 2099186
245 1 0 $a Geometric and nonlinear limit theorems in probability theory.
300 $a 98 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-03(E), Section: B.
500 $a Adviser: Alexander Koldobsky.
502 $a Thesis (Ph.D.)--University of Missouri - Columbia, 2012.
520 $a The concentration of measure phenomenon is a nonlinear equivalent of the law of large numbers that deals with real valued Lipschitz functions and includes linear functionals such as the sample mean. In the first part of this dissertation we study functions that take values in more general metric-like spaces and have the property that they are invariant under coordinate permutations. In Chapter 1 we study functions that take values in the space of convex bodies, in Chapter 2 we study order statistics and in Chapter 3 we prove abstract concentration inequalities for functions taking values in an arbitrary metric space.
520 $a In the second part of the dissertation we study the central limit theorem. We show that if one conditions on certain tail events then convergence to the normal distribution can be achived without having to take a large number of summands. In fact 2 summands is enough.
520 $a The results presented here are taken from the author's papers. In order to streamline the exposition, we have not included all of the results. We urge the reader to consult the published versions when they become available.
590 $a School code: 0133.
650 4 $a Mathematics. $3 515831
650 4 $a Statistics. $3 517247
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0463
690 $a 0364
710 2 $a University of Missouri - Columbia. $b Mathematics. $3 2099187
773 0 $t Dissertation Abstracts International $g 74-03B(E).
790 $a 0133
791 $a Ph.D.
792 $a 2012
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3530878