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Title:Pointwise Relations Between Ergodic Averages and Martingales
Author(s):Goubran, Nader
Doctoral Committee Chair(s):Rosenblatt, Joseph
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.
Issue Date:2002
Type:Text
Language:English
Description:51 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
URI:http://hdl.handle.net/2142/86799
Other Identifier(s):(MiAaPQ)AAI3070310
Date Available in IDEALS:2015-09-28
Date Deposited:2002


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