Pointwise Relations Between Ergodic Averages and Martingales
Goubran, Nader
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https://hdl.handle.net/2142/86799
Description
Title
Pointwise Relations Between Ergodic Averages and Martingales
Author(s)
Goubran, Nader
Issue Date
2002
Doctoral Committee Chair(s)
Rosenblatt, Joseph
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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